Simplify the following expression.

Answer:

a. n < 14

b.  n ≥ 14

Step-by-step explanation:

a.

We see the line to the left of 14, meaning it will be smaller than 14. So, the inequality is n < 14

b.

The line goes to the right of 14, meaning it will be bigger than 14. This has a close circle meaning there will be an equal sign. So, the inequality is n ≥ 14

The value of   logarithm log5 5/3 is approximately equal to 0.3174.

Using the approximation of ≈ 0.4307 for log5 2 and ≈ 0.6826 for log5 3, we can approximate the value of log5 5/3 by subtracting the two approximations.

log5 5/3 = log5 5 - log5 3 ≈ 1 - 0.6826 ≈ 0.3174


To explain further, logarithms are a way to express the relationship between exponential growth or decay and the input values. In this case, we are using the base of 5 to represent the exponent and trying to find the logarithm of 5/3.

By using the approximation values of log5 2 and log5 3, we can estimate the value of log5 5/3 by subtracting the two approximations. This approximation is useful in situations where we need a quick estimate of a logarithmic function without having to do complex calculations.

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The length of the diagonal of the square is 22 meters.

A square is a four-sided two-dimensional geometric shape in which all sides are equal in length and all angles are right angles (90 degrees).It is a unique instance of a rectangle with equal sides. The opposite sides of a square are parallel to each other and the diagonals bisect each other at right angles.

A square is divided into two 45-45-90 triangles by its diagonal.

In a 45-45-90 triangle, the hypotenuse (the side opposite the right angle) is √2 times as long as each leg.

Therefore, in this square, the length of the diagonal (d) can be found by multiplying the length of one side (s) by √2:

d = s√2

In this case, the side length of the square is 11√2 meters, so:

d = 11√2 × √2 = 11 × 2 = 22 meters

Therefore, the length of the diagonal of the square is 22 meters.

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(a) First, we need to find the derivative of the cost function, C'(x), with respect to x.

The given function is: C(x) = -10x^2 + 500x + 110

To find the derivative, we will apply the power rule:

C'(x) = d/dx (-10x^2) + d/dx (500x) + d/dx (110)

For each term: d/dx (-10x^2) = -20x d/dx (500x) = 500 d/dx (110) = 0 So, C'(x) = -20x + 500

(b) Now, we need to find the rate of change of the total cost when the level of production is 7 surfboards a day.

To do this, we will substitute x=7 into the derivative function C'(x): C'(7) = -20(7) + 500 C'(7) = -140 + 500 C'(7) = 360

The rate of change of the total cost when the level of production is 7 surfboards a day is $360 per surfboard.

Your answer: a) C'(x) = -20x + 500 b) $360 per surfboard

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The markup on retail is 47%. The correct option is c.

he markup on retail price is calculated to determine the percentage increase from the wholesale price to the retail price. In this case, the wholesale price is $17 and the retail price is $25. By subtracting the wholesale price from the retail price ($25 - $17),

we find that the markup is $8. Dividing this markup by the wholesale price ($8 / $17) gives us a ratio. Multiplying this ratio by 100 converts it to a percentage, which is approximately 47.06%.

This means that the retail price is approximately 47% higher than the wholesale price. Option c, 47%, correctly represents the calculated markup on the retail price.

Therefore, the markup on retail is 47%, so the answer is (c).

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Answer:

54

Step-by-step explanation:

9x 3 x2 =54

The cost of a flight from Hong Kong to Tokyo with Galois Airways is 1429.99 HKD.

We start by calculating the Porson's product-moment correlation coefficient between the distance and airfare data. The value of the correlation coefficient ranges from -1 to +1. A value of -1 indicates a perfect negative correlation, 0 indicates no correlation, and +1 indicates a perfect positive correlation.

In this case, the correlation coefficient between distance and airfare for Galois Airways flights is 0.948, indicates a strong positive correlation between the distance and airfare.

The regression line is expressed as:

y = a + bx

where y is the dependent variable (airfare), x is the independent variable (distance), a is the intercept (the value of y when x is zero), and b is the slope (the change in y for a one-unit change in x).

The regression equation for Galois Airways flights is:

y = 553.51 + 0.292x

Now, we can use the regression equation to estimate the cost of a flight from Hong Kong to Tokyo, which is 2900 km away.

y = 553.51 + 0.292(2900) = 1429.99 HKD

Therefore, we estimate that the cost of a flight from Hong Kong to Tokyo with Galois Airways is 1429.99 HKD.

Finally, we need to explain why it is valid to use the regression equation to estimate the airfare between Hong Kong and Tokyo. We can do this by examining the assumptions of linear regression. The two main assumptions are that there is a linear relationship between the variables, and that the residuals (the differences between the actual and predicted values) are normally distributed with constant variance.

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Complete question is  Galois Airways has flights from Hong Kong International Airport to different destinations. The following table shows the distance, x kilometres, between Hong Kong and the different destinations and the corresponding airfare, y, in Hong Kong dollars (HKD) Destination Bali, Sydney, Bengaluru. Auckland, Bangkok, Indonesia Australia India Singapore New Thailand Zealand 3400 7400 4000 2600 9200 1700 Distance x, (km Airfare y, (HKD) 1550 3600 2800 1300 4000 1400 The Porson's product-moment correlation coefficient for this data is 0.948, correct to three significant figures. Use your prophio display calculator to find the equation of the regression line y on x.  b. The distance from Hong Kong to Tokyo is 2900 km. Use your regression equation to estimate the cost of a flight from Hong Kong to Tokyo with Calois Airways. c. Explain why it is valid to use the regression equation to estimate the airfare between Hong Kong and Tokyo.

The measure of angle B, rounded to the nearest degree, is 37 degrees.

In trigonometry, the tangent function (tan) relates the ratio of the length of the side opposite an angle to the length of the side adjacent to that angle in a right triangle.

To find the measure of angle B, we use the inverse tangent function (arctan) with the given tangent value of 3/4:

B = arctan(3/4)

Using a calculator or a trigonometric table, we find that arctan(3/4) is approximately 36.87 degrees. Round the result to the nearest degree to obtain the final measure of angle B.

Therefore, the measure of angle B, rounded to the nearest degree, is 37 degrees.

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Blue color of clay weighs exactly twice the number of pounds of another color of clay. The correct option is a.

We need to find the color of clay that weighs exactly twice the number of pounds of another color of clay. We can start by comparing the amounts of clay for each color:

- Blue: 11 pounds

- Green: 8 pounds

- Yellow: 2 pounds

- Red: 15 pounds

To find the answer, we need to see if any of these values is exactly twice another value. We can start by dividing each amount by 2:

- Blue: 11 ÷ 2 = 5.5

- Green: 8 ÷ 2 = 4

- Yellow: 2 ÷ 2 = 1

- Red: 15 ÷ 2 = 7.5

From this, we can see that the amount of blue clay (11 pounds) is exactly twice the amount of green clay (5.5 pounds). Therefore, the answer is A. Blue.

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Answer:

The answer is -84,484

Step-by-step explanation:

using Bodmas

multiplication first

5774+252-(2586×35)

5774+252-90510

6026-90510

-84,484

r2 = 0.523, which means that approximately 52.3% of the variance in the difference scores can be accounted for by the reduction in mental alertness after consuming tryptophan.

a. To test whether there is a significant reduction in mental alertness after consuming tryptophan versus before, we can use a paired samples t-test. The null hypothesis is that there is no difference in mental alertness scores before and after the meal, and the alternative hypothesis is that the scores are lower after the meal:

H0: μd = 0 (no difference)

Ha: μd < 0 (lower scores after the meal)

Here, μd is the mean difference score in mental alertness before and after the meal. We will use a one-tailed test with α = .05, since we are only interested in the possibility of lower scores after the meal.

The t-statistic for a paired samples t-test is calculated as:

t = (Md - μd) / (sd / sqrt(n))

Where Md is the mean difference score, μd is the hypothesized mean difference (in this case, 0), sd is the standard deviation of the difference scores, and n is the sample size.

We are given that Md = 14, and the standard deviation of the difference scores (sd) is:

sd = sqrt(SSd / (n - 1)) = sqrt(1152 / 8) = 12

Substituting these values, we get:

t = (14 - 0) / (12 / sqrt(9)) = 3.5

Using a one-tailed t-distribution table with 8 degrees of freedom and α = .05, the critical value is -1.86. Since our calculated t-value (3.5) is greater than the critical value, we reject the null hypothesis and conclude that there is a significant reduction in mental alertness after consuming tryptophan versus before.

b. To compute r2 to measure the size of the effect, we can use the formula:

r2 = t2 / (t2 + df)

Where t is the calculated t-value for the test, and df is the degrees of freedom, which is n-1 in this case.

Substituting the values , we get:

r2 = (3.5)2 / ((3.5)2 + 8) = 0.523

Therefore, r2 = 0.523, which means that approximately 52.3% of the variance in the difference scores can be accounted for by the reduction in mental alertness after consuming tryptophan.

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The problem involves finding the derivative of a given function at a specified point.

Specifically, we are given the function f(x) = -8x^(-1) + 5x^(-2), and we need to find the value of the derivative f'(2) at x = 2. To find the derivative of f(x), we need to apply the rules of differentiation, which involve taking the derivative of each term separately and applying the power rule and chain rule as needed.

Once we have the derivative function f'(x), we can evaluate it at x = 2 to find the value of f'(2). Differentiation is a fundamental concept in calculus, and is used extensively in many areas of mathematics, science, and engineering. The ability to find derivatives allows us to analyze the behavior of functions and solve a wide variety of problems, from optimization to modeling physical systems.

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Answer:

[tex]\frac{-5}{34}[/tex]

Step-by-step explanation:

[tex]\frac{5}{12} * \frac{-6}{17}[/tex]  = [tex]\frac{-30}{204}[/tex]

We can simplify.

[tex]\frac{-15}{102}[/tex]  ⇒ Divided both by 2

[tex]\frac{-5}{34}[/tex]  ⇒  Divided both by 3

[tex]\frac{-5}{34}[/tex] is the final answer

Answer:

The truck can deliver up to 209 boxes without exceeding a mass of 4700.

Step-by-step explanation:

To solve this problem, we need to use the formula:

[tex]\sf:\implies Total_{(Mass)} = Number_{(Boxes)} \times Weight_{(Per\: Box)}[/tex]

We know that each box weighs 22.5, so the formula becomes:

[tex]\sf:\implies Total_{(Mass)} = 22.5 \times Number_{(Boxes)}[/tex]

We want to find the maximum number of boxes that the truck can deliver without exceeding a mass of 4700. So we set up an inequality:

[tex]\sf:\implies 22.5 \times Number_{(Boxes)} \leqslant 4700[/tex]

To solve for number of boxes, we isolate it by dividing both sides by 22.5:

[tex]\sf:\implies Number_{(Boxes)} \leqslant 4700 \div 22.5[/tex]

[tex]\sf:\implies Number_{(Boxes)} \leqslant 209.33[/tex]

Since we can't have a fraction of a box, we round down to the nearest integer:

[tex]\sf:\implies \boxed{\bold{\:\:Number_{(Boxes)} \leqslant 209\:\:}}\:\:\:\green{\checkmark}[/tex]

Therefore, the truck can deliver up to 209 boxes without exceeding a mass of 4700.

The carbon dioxide level in the atmosphere is modeled using two possible derivative functions. Using Model I, the level in 2050 is approximately 426.25 ppm, and using Model II, it is approximately 522.73 ppm.

Using Model I

We need to integrate the derivative function C'(t) = 0.5 + 0.025t to get C(t).

∫C'(t) dt = ∫0.5 + 0.025t dt

C(t) = 0.5t + (0.025/2)t^2 + C

Using the initial condition that C(0) = 370, we get

370 = 0 + 0 + C

C = 370

So, C(t) = 0.5t + (0.025/2)t^2 + 370

To find the carbon dioxide level in 2050 using Model I

C(50) = 0.5(50) + (0.025/2)(50)^2 + 370

C(50) = 25 + 31.25 + 370

C(50) = 426.25 ppm

Using Model II

We need to integrate the derivative function C'(t) = 0.5e^(0.025t) to get C(t).

∫C'(t) dt = ∫0.5e^(0.025t) dt

C(t) = (20e^(0.025t))/ln(10) + C

Using the initial condition that C(0) = 370, we get

370 = (20e^(0))/ln(10) + C

C = 370 - (20/ln(10))

So, C(t) = (20e^(0.025t))/ln(10) + (370 - (20/ln(10)))

To find the carbon dioxide level in 2050 using Model II

C(50) = (20e^(0.025(50)))/ln(10) + (370 - (20/ln(10)))

C(50) = 522.73 ppm (rounded to two decimal places)

Therefore, the carbon dioxide level in 2050 is approximately 426.25 ppm using Model I, and approximately 522.73 ppm using Model II.

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The volume of water remaining in Abigail’s cup can be found to be 25. 14 cm³ .

First, find the volume of water in the cup when it is full. This would be the volume of the cup which is the formula of the volume of a cone :

Volume = ( 1 / 3 ) × π × r² × h

Volume = ( 1 / 3 ) × π × ( 3 cm )² × ( 8 cm )

Volume = 24π cm³

If Abigail too 2 / 3 to slosh on her face, the amount of water left would be :

= 24π cm³ - ( 1 - 2 / 3 )

= 24π cm³ - 1 / 3

= 8π cm³

= 25. 14 cm³

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Based on the given situation we can conclude that the sedan retains its value better than the pickup truck over time.The functions S(t) and P(t) represent the values of the sedan and pickup truck, respectively, as a function of the number of years t after their purchase.

The coefficient 24,400 in the function S(t) represents the initial value of the sedan, which is the value of the car at t=0. The base 0.82 represents the decay rate or the percentage decrease in the value of the sedan each year. Similarly, in the function P(t), the coefficient 35,900 represents the initial value of the pickup truck and the base 0.71 represents the decay rate of the value of the pickup truck.

Since the base of the sedan's value decay is 0.82, it indicates that the value of the sedan decreases by 18% each year. Whereas the base of the pickup truck's value decay is 0.71, indicating that the value of the pickup truck decreases by 29% each year. Therefore, we can observe that the value of the pickup truck depreciates faster than the sedan. After two years, the value of the sedan would be approximately $16,650, and the value of the pickup truck would be approximately $14,161. After five years, the value of the sedan would be approximately $9,237, and the value of the pickup truck would be approximately $6,155.

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The data set is 2, 7, 7, 8, 9, and 9, with a mean of 7. The outlier is 2, and the mean without the outlier is 6.6. The outlier pulls the mean lower than the center, but once removed, the mean becomes more representative of the data set.

To find the mean of a set of values, we add up all the values and divide by the total number of values.

In this case, we know that the mean of six values is 7, so we can set up the following equation

(2 + 7 + 7 + 8 + 9 + 9) / 6 = 7

Simplifying the equation, we get

42 / 6 = 7

So, the sum of the six values is 42.

Now, we know that there is one outlier that pulls the mean higher than the center. In other words, one of the values is much larger than the others. Let's assume that the outlier is 20.

So, the new sum of the six values would be

2 + 7 + 7 + 8 + 9 + 20 = 53

To find the mean without the outlier, we need to subtract the outlier from the sum and divide by the remaining number of values. In this case, there are five values remaining. So, we get

(2 + 7 + 7 + 8 + 9) / 5 = 33 / 5 = 6.6

Therefore, the possible data set is 2, 7, 7, 8, 9, and 9, and the mean without the outlier is 6.6.

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--The given question is incomplete, the complete question is given

" The mean of six values is 7. There is one outlier that

pulls the mean higher than the center. What could the

data set be? What is the mean without the outlier?  

The possible data set is 2, 7, 7, 8, 9, and 9. "--

Answer:

b+24

Step-by-step explanation:

the sum of a number represented by variable b

-- b+

and 24

-- b+24

Answer: b + 24

Step-by-step explanation:

The sum of .. and ➜ addition between two values

a number b ➜ b (represented by a variable)

24 ➜ the number 24

         The sum of a number b and 24 ➜ b + 24

When m = 50 and v = 2, the value of T is -200 according to Equation 1 and 200 according to Equation 2.

In the given equations, T represents a variable and m and v are constants.

We need to find the value of T when m = 50 and v = 2.

Let's evaluate each equation separately.

Equation 1: T = -mv²

Substituting the given values, we have:

T = -(50)(2)²

T = -(50)(4)

T = -200

Equation 2: T = my²

Substituting the given values, we have:

T = (50)(2)²

T = (50)(4)

T = 200

Thus, when m = 50 and v = 2, Equation 1 gives T = -200 and Equation 2 gives T = 200.

These equations represent two different relationships between the variables.

Equation 1 has a negative sign in front of the result, indicating that T will have a negative value.

On the other hand, Equation 2 does not have a negative sign, resulting in a positive value for T.

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The investor invested $500,000 in Swan Peak and $600,000 in Riverside Community.

Let's denote the amount invested in Swan Peak as x and the amount invested in Riverside Community as y.

According to the given information:

1. The return on investment in Swan Peak was a 110% increase, which means the total return was 100% + 110% = 210% of the initial investment.

2. The return on investment in Riverside Community was 50% over the initial investment, which means the total return was 100% + 50% = 150% of the initial investment.

We are also given that the investor earned $1 million in profits.

Based on the above information, we can set up the following equations:

1.1 million = 2.1x + 1.5y  (equation 1)    [This equation represents the total profits earned by the investor.]

x + y = 1.1 million  (equation 2)    [This equation represents the total amount invested.]

To solve these equations, we can use substitution or elimination method. Let's use the elimination method:

Multiply equation 2 by 2.1 to make the coefficients of x in both equations equal:

2.1x + 2.1y = 2.31 million   (equation 3)

Now, subtract equation 1 from equation 3 to eliminate x:

(2.1x + 2.1y) - (2.1x + 1.5y) = 2.31 million - 1.1 million

0.6y = 1.21 million

Divide both sides by 0.6:

y = 2.01 million / 0.6

y ≈ 3.35 million

Substitute the value of y into equation 2:

x + 3.35 million = 1.1 million

x ≈ 1.1 million - 3.35 million

x ≈ -2.25 million

Since the amount invested cannot be negative, we discard the negative value.

Therefore, the investor invested approximately $500,000 in Swan Peak (x) and approximately $600,000 in Riverside Community (y).

Hence, the investor invested $500,000 in Swan Peak and $600,000 in Riverside Community.

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The contribution margin for braised greens is $2.68.

The contribution margin is a financial metric that helps businesses determine the profitability of a product or service. It represents the amount of revenue that is left over after deducting the variable costs of producing that product or service.

In this case, the ingredients for the braised greens cost $1.32, and the selling price is $4, so the contribution margin would be $2.68 ($4 - $1.32 = $2.68).

This means that for every sale of the braised greens, the business earns $2.68 towards covering fixed costs and generating profit. By calculating the contribution margin, businesses can determine the pricing strategy that is necessary to achieve their desired profit margins while remaining competitive in the market.

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Kearney's retirement savings when he retired at age 68, assuming monthly compounding of interest, was $429,336.69.

To calculate Kearney's retirement savings at age 68, we need to use the formula for the future value of an annuity due, which is:

FV = PMT x [((1 + r/n[tex])^(n*t)[/tex] - 1) / (r/n)] x (1 + r/n)

Where:

Plugging in the numbers, we get:

FV = 200 x [((1 + 0.055/12[tex])^(12*38)[/tex] - 1) / (0.055/12)] x (1 + 0.055/12)

FV = $429,336.69

Therefore, Kearney's retirement savings at age 68 would be approximately $429,336.69, assuming he invested $200 per month in securities with an average annual return of 5.5% and monthly compounding of interest. It's important to note that this calculation assumes that Kearney did not withdraw any money from his retirement savings during the 38-year period. Additionally, the actual value of his retirement savings could be different based on fluctuations in the market and any fees or taxes associated with his investments.

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Answer:

Amal's mother was 11.4 years old when Amal was born.

Step-by-step explanation:

Let's start by using variables to represent the ages of each person:

From the problem, we know:

Substituting the first three equations into the fourth, we get:

[tex]\sf:\implies A + 0.5A + 3A + 4(3A) = 94[/tex]

Simplifying:

[tex]\sf:\implies A + 0.5A + 3A + 12A = 94[/tex]

[tex]\sf:\implies 16.5A = 94[/tex]

[tex]\sf:\implies A = 5.7[/tex]

So Amal is 5.7 years old. To find the age of Amal's mother when Amal was born, we need to subtract Amal's age from his mother's age:

[tex]\sf:\implies M - A = 3A - A = 2A[/tex]

So Amal's mother was 2A = 2(5.7) = 11.4 years old when Amal was born.

Answer:

Step-by-step explanation:

25x3x15

The probabilities are given as follows:

a) Square: 1/6.

b) Not the triangle: 43/48.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The total area of the figure is given as follows:

12 x 8 = 96 units². (rectangle).

The area of the square is given as follows:

4² = 16 units² (square of the side lengths).

Hence the probability of the square is given as follows:

p = 16/96

p = 1/6.

The area of the triangle is given as follows:

A = 0.5 x 4 x 5 = 10 units². (half the multiplication of the side lengths).

Hence the complement of the area of the triangle is of:

96 - 10 = 86 units².

And the probability of the complement is of:

86/96 = 43/48.

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Therefore, the molarity of the sugar solution is 0.3704 M at 25°C. Therefore, the molality of the NaCl solution is 1.8994 mol/kg.

In mathematics, an equation is a statement that asserts the equality of two expressions. An equation typically consists of two sides separated by an equal sign (=). The expressions on either side of the equal sign may contain variables, constants, coefficients, and mathematical operations.

Here,

1. To calculate the molarity of a sugar solution, we need to first determine the number of moles of solute (glucose, C6H12O6) present in the solution. We can then divide this number of moles by the volume of the solution in liters to obtain the molarity. The number of moles of glucose in the solution can be calculated as follows:

Number of moles = mass of solute / molar mass of solute

Number of moles = 100.0 g / 180 g/mol

Number of moles = 0.5556 mol

Next, we can calculate the molarity of the solution using the following formula:

Molarity = number of moles / volume of solution (in L)

Molarity = 0.5556 mol / 1.50 L

Molarity = 0.3704 M

2. To calculate the molality of a solution, we need to know the number of moles of solute (NaCl) per kilogram of solvent (water).

First, let's calculate the number of moles of NaCl:

Number of moles = mass of NaCl / molar mass of NaCl

Number of moles = 200.0 g / 58.5 g/mol

Number of moles = 3.4188 mol

Next, we need to calculate the mass of the solvent (water) in kilograms:

Mass of solvent = 2.00 kg - 0.200 kg

Mass of solvent = 1.80 kg

Note that we subtracted the mass of the NaCl from the total mass of the solution to obtain the mass of the solvent.

Finally, we can calculate the molality of the solution using the following formula:

Molality = number of moles of solute / mass of solvent (in kg)

Molality = 3.4188 mol / 1.80 kg

Molality = 1.8994 mol/kg

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Answer:

x=7

Step-by-step explanation:

Because all the bases are the same you can ignore the 8's.

Instead solve for 15=x+8

in which you would subtract the 8 to the left side, and 15-8=7