Answer:
a. y = 2(x + 3)² - 17
b. y = 4(x + 6)² - 154
Step-by-step explanation:
a. y = 2x² + 12x + 1
y = 2[(x² + 6x)] + 1
y = 2[(x + 3)² - 9] + 1
y = 2(x + 3)² - 18 + 1
y = 2(x + 3)² - 17
b. y = 4x² + 48x - 10
y = 4[(x² + 12x)] - 10
y = 4[(x + 6)² - 36)] - 10
y = 4(x + 6)² - 144 - 10
y = 4(x + 6)² - 154
The image of ΔABC after a reflection across Line E G is ΔA'B'C'.
2 triangles are shown. Line E G is the line of reflection. Line segment D D prime has a midpoint at point F. Line segment C C prime has a midpoint at point G. Points B and B prime share a point. Angle C G F is a right angle.
Which triangle must be a right triangle and why?
ΔA'B'C' is right because it is the image of ΔABC.
ΔADC is right because AA' intersects AC at A.
ΔBCC' is right because B lies of the line of reflection.
ΔBGC is right because Line E G is perpendicular-to CC'.
Δ DGC is right angled triangle because Line E G is perpendicular-to CC', Option D is the correct answer.
What is Triangle ?Triangle is a polygon with three sides , angles and vertices.
It is given that the there are two Triangles , ABC and A'B'C' as an image of the ABC
* Line segment AA' has a midpoint at point F
*D is the mid point of the line joining BB' .*
The figure is attached with the answer.
the line of reflection of the object is always perpendicular to the object and the image.
it is also given that CGF is a right angle.
Therefore triangle DGC is right angled triangle , (the option given in the question is incorrect ) , Line E G is perpendicular-to CC'.
Option D is the correct answer.
Please Refer to the image for correct coordinates.
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Chloe bought an equal number of forks and spoons for a party. The forks were sold at 3 for 2$ and the spoons were sold at 4 for 3$. She spent 5$ more on spoons than on forks. How much did she spend altogether?
60 forks 60÷3=$20
60 spoons 60÷4=$15
$20+$15=$35 total spent for forks and spoons
Which equation represents a side that is perpendicular to side d? O y = 2x+5 Oy=-2x+5 NG 0 Y=2x-5/2 OY--12-12 = Which equation represents a side that is perpendicular to side d ? O y = 2x + 5 Oy = -2x + 5 NG 0 Y = 2x - 5 / 2 OY -- 12-12 =
The equation represents a side that is perpendicular to side d is y = -2x+5. Option B is correct.
What is the slope?A numerical assessment of a line's angle relative to the ground is known as the slope.
The inclination of any line, ray, or line segment is the fraction of the perpendicular to the horizontal distance between any two positions on it.
The given linear equation in the problem is;
y = 2x+5
Compare the equation with the standard equation;
[tex]\rm y = mx+ c[/tex]
where,
m is the slope and c is the intercept. After comparing, we will get; Hence, the slope and y-intercept will be;
m = 2
The product of the slope of the two-line perpendicular to each will be -1.
m₁×m₂ = -1
The equation represents a side that is perpendicular to side d is;
y = -2x+c.
m₁=2
m₂=-2
m₁×m₂ = -1
The equation represents a side that is perpendicular to side d is y = -2x+5.
Hence, option B is correct.
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Can I have the solution with steps
Answer:
1/6
Step-by-step explanation:
As usual in trigonometry, there are so many relationships between the trigonometric functions, there is bound to be more than one method to arrive at the answer.
Knowing values for the sine and cosine function for certain angles on the unit circle proves to be quite helpful. In general, I recommend 0°, 30°, 45°, 60°, and 90° at a minimum.
Recall the following 6 things:
[tex]\cos(30^o)=\frac{\sqrt{3}}{2}[/tex][tex]\cos(60^o)=\frac{1}{2}[/tex][tex]\sin(30^o)=\frac{1}{2}[/tex][tex]\sin(60^o)=\frac{\sqrt{3}}{2}[/tex][tex]\tan(\theta)=\dfrac{\sin(\theta)}{\cos(\theta)}[/tex][tex]\tan^2(\theta)=\tan(\theta)\tan(\theta)[/tex]Knowing these 6 things (4 things from the unit circle, a way to write the tangent function in terms of sine and cosine, and the definition of a squared trig function), we can simplify the given expression down to a single number:
The definition of the tangent squared function is that the output of the tangent function is squared...
[tex]\dfrac{1-\tan^2(30^o)}{1+\tan^2(60^o)}=\dfrac{1-(\tan(30^o))^2}{1+(\tan(60^o))^2}[/tex]
Using fact 5, and turning the tangent function into sines and cosines...
[tex]=\dfrac{1-\left(\frac{\sin(30^o)}{\cos(30^o)}\right)^2}{1+\left(\frac{\sin(60^o)}{\cos(60^o)}\right)^2}[/tex]
Using facts 1-4, and substituting known values for sines and cosines...
[tex]=\dfrac{1-\left(\frac{(\frac{1}{2})}{(\frac{\sqrt{3}}{2})}\right)^2}{1+\left(\frac{(\frac{\sqrt{3}}{2})}{(\frac{1}{2})}\right)^2}[/tex]
Division is multiplication by the reciprocal...
[tex]=\dfrac{1-\left(\frac{1}{2}*\frac{2}{\sqrt{3}}\right)^2}{1+\left(\frac{\sqrt{3}}{2}*\frac{2}{1}\right)^2}[/tex]
Reducing/simplifying common factors of 2...
[tex]=\dfrac{1-\left(\frac{1}{\sqrt{3}}\right)^2}{1+(\sqrt{3})^2}[/tex]
Squaring a square root...
[tex]=\dfrac{1-\left(\frac{1}{3}\right)}{1+(3)}[/tex]
Finding a common denominator...
[tex]=\dfrac{\frac{3}{3}-\frac{1}{3}}{4}[/tex]
Definition of subtracting fractions...
[tex]=\dfrac{\frac{3-1}{3}}{4}[/tex]
Arithmetic...
[tex]=\dfrac{\frac{2}{3}}{4}[/tex]
Division is multiplication by a reciprocal...
[tex]=\dfrac{2}{3}*\dfrac{1}{4}[/tex]
Simplification and reducing the fraction...
[tex]=\dfrac{1}{6}[/tex]
So, [tex]\dfrac{1-\tan^2(30^o)}{1+\tan^2(60^o)}=\dfrac{1}{6}[/tex]
Please help me on this question!
Answer:
u = 10 ft
Step-by-step explanation:
cuboid volume = w × h × l
width * hight * length
560 = 7 × 8 × u
u = 10 ft
Answer:
u = 10 ft
Step-by-step explanation:
Volume of a rectangular prism = lwh
where:
l = lengthw = widthh = heightGiven:
Volume = 560 ft³width = 7 ftlength = 8 ftheight = uSubstitute the given values into the formula and solve for h:
⇒ 560 = 8 × 7 × u
⇒ 560 = 56u
⇒ 56u ÷ 56 = 560 ÷ 56
⇒ u = 10 ft
Therefore, the height of the prism is 10 ft.
which of the following must be true?
Answer:
C
Step-by-step explanation:
Answer C is correct. The absolute value of 10 is 10 and that of -10 is 10. Same result.
36 students for 3 teachers =
1.0
5
12 students for 1 teacher.
Answer:
12
Step-by-step explanation:
36 divided by 3 =12 for 1 teacher
Peter's dog weighs 12 pounds more than Joe's dog. The dogs weigh 36
pounds all together. Write an equation to find the weight of Joe's dog.
Which equation represents the graph below?
Answer:
D
Step-by-step explanation:
The slope-intercept form is the equation of a straight line (y=mx+b)
m= gradient and b= y-intercept
m=2/3 (rise over run) b= 4 (it goes through the point (0,4)
y=(2/3)x+4
Get rid of the fraction by multiplying everything by 3
3y=2x+12
which is also -2x+3y=12
Maria is on a hike. if she hikes to the scenic lookout on the following map first, she will have to hike farther than if she went straight to the end of the hike. 3 connected points on a coordinate plane. the point labeled, "maria," is at 4, -4. the point labeled, "end," is at -5, 5. a solid line connect the points "maria" and "end." the point labeled, "scenic lookout," is at 2, 3. dashed lines connect "maria" to "scenic lookout" and connect "scenic lookout" to "end." coordinate values on the map are in kilometers. how much shorter is the path straight to the end of the hike than past the scenic lookout? round your final answer only to the nearest kilometer. \text{km}kmstart text, k, m, end text
The path straight to the end of the hike is 6 km farther than past the scenic lookout.
How to determine the difference in the parts?The map is not given, but the question can still be answered
From the question, the positions are given as::
Maria = (4, -4)
Scenic = (2, 3)
End = (-5, 5)
The distance between Maria and the end point is calculated using:
[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2[/tex]
So, we have:
[tex]Route\ 1 = \sqrt{(4 + 5)^2 + (-4 -5)^2}[/tex]
[tex]Route\ 1 = 13[/tex]
The distance between Maria and the scenic lookout is calculated using:
[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2[/tex]
So, we have:
[tex]Route\ 2 = \sqrt{(4 - 2)^2 + (-4 -3)^2}[/tex]
[tex]Route\ 2 = 7[/tex]
The distance between both routes is:
Distance = 13 - 7
Evaluate
Distance = 6
Hence, the path straight to the end of the hike is 6 km farther than past the scenic lookout.
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How much is the bill for a person who used 700 kWh in a month?
Answer:
700 kWh which is more than 200 so
0.10(x - 200) + 30
0.10( 700 -200)+ 30
0.10( 500) + 30
50 + 30
80
$80
question below
What matrix is the result of m*H?
Enter your answer by filling in the boxes. Enter any fractions as simplified fractions.
Answer:
[tex]m \times H=\left[\begin{array}{c c c}\boxed{-9} & \boxed{36} & \boxed{-\dfrac{9}{2}}\end{array}\right][/tex]
Step-by-step explanation:
Calculate the value of m
Given:
[tex]3\left[\begin{array}{c c}-1 & 2 \\4 & 8\end{array}\right]=\dfrac{2}{3}m \times \left[\begin{array}{c c}-1 & 2 \\4 & 8\end{array}\right][/tex]
Therefore:
[tex]\implies 3=\dfrac{2}{3}m[/tex]
[tex]\implies m=3 \times \dfrac{3}{2}[/tex]
[tex]\implies m=\dfrac{9}{2}[/tex]
Calculate the value of H
Given:
[tex]\left(H+ \left[\begin{array}{c c c}1 & 4 & -2\end{array}\right]\right)+\left[\begin{array}{c c c}3 & 2 & -6\end{array}\right]=\left[\begin{array}{c c c}-2 & 8 & -1\end{array}\right]+\left(\left[\begin{array}{c c c}1 & 4 & -2\end{array}\right]+\left[\begin{array}{c c c}3 & 2 & -6\end{array}\right]\right)[/tex]
Therefore:
[tex]\implies H= \left[\begin{array}{c c c}-2 & 8 & -1\end{array}\right][/tex]
Calculating m × H
[tex]\implies m \times H=\dfrac{9}{2} \times \left[\begin{array}{c c c}-2 & 8 & -1\end{array}\right][/tex]
[tex]\implies m \times H=\left[\begin{array}{c c c}\dfrac{9}{2}(-2) & \dfrac{9}{2}(8) & \dfrac{9}{2}(-1)\end{array}\right][/tex]
[tex]\implies m \times H=\left[\begin{array}{c c c}-9 & 36 & -\dfrac{9}{2}\end{array}\right][/tex]
What is the best name for the part of the figure
identified by the arrow?
O line of reflection
O line of symmetry
O plane of reflection
O axis of symmetry
The best name for the part of the figure identified by the arrow is the plane of reflection option third is correct.
What is geometric transformation?It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.
We have given a three-dimensional figure.
As we can see the arrow is pointing at the plane.
A triangular prism is reflected over the given plane and creates a mirror image of a triangular prism.
A plane is a plane of symmetry.
Thus, the best name for the part of the figure identified by the arrow is the plane of reflection option third is correct.
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Adam wins $30 in a "spot the ball" competition. He decides to save the money and opens a saving account with the $30. After his win, he continues to put $8 into his savings account each week. Identify a rule for the linear function that describes Adam's savings. Use the rule to find the amount Adam saved during the first 5 weeks.
Answer:
$110
Step-by-step explanation:
$30-$8=$22 each week
$22×5weeks=$110
La siguiente operación 147.3 = 441 es una:
División b- Sustracción c- Multiplicación
plis necesito la respuesta ahora dare estrellas lo juro
La operación que representa 147.3 = 441 es dada por una multiplicación, por eso opción c es correcta.
¿Qué operación está representada por 147 . 3 = 441?El resultado del producto entre 147 y 3 es de 441, por lo que se hace una operación de multiplicación.
Así, hay que la opción c es correcta.
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The function f(x) = -√x is shown on the graph.
-6
43
4-
N
-7-6-5-4-3-2-₁ 1 2 3 4 5 6 7 x
-2+
-3-
-4
Which statement is correct?
The domain of the function is all real numbers less
than or equal to -1.
The range of the function is all real numbers greater
than or equal to 0.
O The range of the function is all real numbers less
than or equal to 0.
The domain of the function is all real numbers less
than or equal to 0.
Answer: The range of the function is all real numbers less
than or equal to 0.
The correct statement for the given function f(x) = -√x is "The range of the function is all real numbers less than or equal to 0." So, the correct option is C.
The domain of the function is all real numbers that are greater than or equal to 0 but we know that the square root of a negative number is in the real number system.
The graph of the function shows that for each positive input i.e. the range values we get the output values that are negative or zero.
Therefore, the range of the function is all real numbers less than or equal to 0, which is option C.
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find the area of the rectangle below
(3x+4) feet x
(x+3) feet
select the correct answer
Answer:
3x^2+ 13x + 12
Step-by-step explanation:
Multiply the length and width:
(3x+4) * (x+3)
FOIL method:
3x^2 + 9x + 4x + 12
Combine like terms
3x^2+ 13x + 12
3x[tex]3x^{2} +8x-10[/tex]
The solution to the quadratic equation 3x² + 8x - 10 by using the quadratic formula is x = 0.927 or -3.594
Solving quadratic equations.Quadratic equations are algebraic expressions that are represented in the power of the second degree. They usually take the form ax² + bx + c
From the given information, we are to solve the quadratic equation:
3x² + 8x - 10Using the quadratic formula:
[tex]\mathbf{=\dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}}[/tex]
where:
a = 3b = + 8c = - 10[tex]\mathbf{= \dfrac{-(8)) \pm \sqrt{(8)^2 - 4(3 \times (-10))}}{2(3)}}[/tex]
[tex]\mathbf{= \dfrac{-(8)) \pm \sqrt{64 -4 (-30)}}{6}}[/tex]
[tex]\mathbf{= \dfrac{-(8)) \pm \sqrt{64+120}}{6}}[/tex]
x = 0.927 or -3.594
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The nth term of a sequence is -2n - 4. Work out the 50th term of the sequence.
Answer:
-104
Step-by-step explanation:
1) Substitute 50 into n.
-2(50) - 4
-100 - 4
-104
If f(x) = 4x² + 1 and g(x)=x2-5, find (f- g)(x).
Answer:
3x² +6
Step-by-step explanation:
(f-g)(x) = f(x) -g(x) = (4x²+1) -(x²-5) . . . . . substitute the function definitions
... = 4x² +1 -x² +5 . . . . . . . . . . . eliminate parentheses
... = (4-1)x² +(1+5) . . . . . . . . . . . collect like terms
... = 3x² +6
Anne is visiting a friend who lives 18.5 km away. She travels 10 km by
train, 1.5 km by bus, and walks the rest of the way. If she walks at a rate
of 3.5 km per hour, for how long will Anne walk?
Answer:
Anne will walk for 2 hours.
Step-by-step explanation:
Distance formula = velocity × time
Total distance is 18.5 km
Anne travels by train = 10 km
and by bus = 1.5 km
let the distance covered by anne by walking be x
10 + 1.5 + x = 18.5
x = 18.5 - 10 - 1.5
x = 7km
Rate of walking is 3.5 km per hour
the time she will take while walking = 7 ÷ 3.5 = 2 hours.
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which of the following is a rational number
a.√5
b.π
c.1/2
d.√(77)
In a certain region of space, the potential is given by v=2x−5x2y 3yz2. How much is the magnitude of the electric field at point (-2, 2, 0)?
The magnitude of the electric field at the point (-2, 2, 0) is 46.52 V/m
How to calculate the electric field?Since in a certain region of space, the potential is given by v = 2x − 5x²y 3yz²,
The electric field, E = -grad(V) where grad(V) = (dV/dx)i + (dV/dy)j + (dV/dz)k
Since V = 2x − 5x²y + 3yz²
dV/dx = d(2x − 5x²y + 3yz²)/dx
= d2x/dx - d5x²y/dx + d3yz²/dx
= 2 - 10xy + 0
= 2 - 10xy
dV/dy = d(2x − 5x²y + 3yz²)/dy
= d2x/dy - d5x²y/dy + d3yz²/dy
= 0 - 5x² + 3z²
= - 5x² + 3z²
dV/dz = d(2x − 5x²y + 3yz²)/dz
= d2x/dz - d5x²y/dz + d3yz²/dz
= 0 - 0 + 6z
= 6z
The electric field
So, E = -grad(V)
= -[(dV/dx)i + (dV/dy)j + (dV/dz)k]
= -[(2 - 10xy)i + (- 5x² + 3z²)j + (6z)k]
So, the electric field at (-2, 2, 0) is
E = -[(2 - 10xy)i + (- 5x² + 3z²)j + (6z)k]
E = -[(2 - 10(-2)(2))i + (- 5(2)² + 3(0)²)j + (6(0))k]
E = -[(2 + 40)i + (- 5(4) + 0)j + (0)k]
E = -[42i + (-20 + 0)j + (0)k]
E = -[42i - 20j + 0k]
E = -42i + 20j - 0k
The magnitude of the electric field
So, the magnitude of E at (-2, 2, 0) is
|E| = √[(-42)² + 20² + 0²]
= √[1764 + 400 + 0]
= √2164
= 46.52 V/m
So, the magnitude of the electric field at the point (-2, 2, 0) is 46.52 V/m
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Please answer both questions math
Answer:
[tex]3[/tex] and perpendicular
Step-by-step explanation:
It's important to remember that equations of lines are always set up in the format of [tex]y=mx+c[/tex].
[tex]y[/tex] is the [tex]y[/tex] value, [tex]m[/tex] is the gradient/slope, [tex]x[/tex] is the [tex]x[/tex] value and [tex]c[/tex] is the y-intercept.
Therefore, we must always rearrange our line equations so that [tex]y[/tex] is the subject.
In the first question, we are given the equation [tex]2x+6y=12[/tex].
We rearrange to make [tex]y[/tex] the subject:
[tex]6y = 12-2x[/tex]
Then, we divide both sides by 6 to have the [tex]y[/tex] isolated:
[tex]\frac{6}{6} y = \frac{12}{6} - \frac{2}{6}x\\\\ y = 2 - \frac{1}{3}x[/tex]
To find a perpendicular slope, we use the negative reciprocal of the original slope. The negative part of that means we negate the value (it becomes inverse) and the reciprocal part means that we flip the fraction.
So here, the slope is [tex]-\frac{1}{3}[/tex].
So, the negative reciprocal of that would be [tex]3[/tex] because we inverse the sign (the negative becomes positive) and the fraction is flipped to create [tex]\frac{3}{1}=3[/tex].
So, the perpendicular slope is [tex]3[/tex].
In the second question, we have two equations. They both need to be rearranged to isolate the [tex]y[/tex].
[tex]4x-y=5\\4x = 5 + y\\y = 4x - 5\\\\4y = -x-12\\y = -\frac{1}{4}x - 3[/tex]
Look at the slopes of the two equations. If you look carefully, you will see that they are inverse of each other (one is positive and one is negative) and if you imagine [tex]4 = \frac{4}{1}[/tex], the fraction is flipped.
This means that the values are negative reciprocals of each other, meaning the lines are perpendicular.
If F= {(1,5), (4, 1), (2, 7)}and g= {(3, 1), (5 4) (-6,2)} represent fog in mapping of agram and to find fog in ordered pair form
From the given mappings, we have
[tex]f(1) = 5, f(4) = 1, f(2) = 7[/tex]
and
[tex]g(3) = 1, g(5) = 4, g(-6) = 2[/tex]
Then the composition of [tex]f[/tex] with [tex]g[/tex], or [tex]f\circ g[/tex], is
[tex]\boxed{f\circ g = \{(3,5), (5,1), (-6, 7)\}}[/tex]
since
[tex]g(3) = 1 \implies (f\circ g)(3) = f(g(3)) = f(1) = 5[/tex]
[tex]g(5) = 4 \implies (f\circ g)(5) = f(4) = 1[/tex]
[tex]g(-6) = 2 \implies (f\circ g)(-6) = f(2) = 7[/tex]
What is the area of rectangle ABCD?
coordinate plane with rectangle ABCD at A 0 comma negative 1, B 0 comma 4, C 4 comma 4, and D 4 comma negative 1
Answer:
Area = 20 units
Step-by-step explanation:
A (-1,0)
B (0,4)
C (4,4)
D (4,-1)
i hope this is right
Answer:
Area = 20
Step-by-step explanation:
A (0,-1)
B (0, 4)
C (4, 4)
D (4, -1)
What are the domain and range of the function below?
A. Domain: (-4,0)
Range: [-2,∞)
B. Domain: (-3,0)
Range: [-2,∞)
C. Domain: (-∞,∞)
Range: [-2,∞)
D. Domain:
Range: (-∞,∞)
PS don't mind that dot on the graph, didn't mean to put it there.
The domain is (-∞,∞) and the range is [-2,∞)
How to determine the domain and the range?From the graph, we can see that the x values extend at both sides of the graph.
This means that the domain is the set of real values i.e. (-∞,∞)
However, the minimum y value is -2 and it increases from their
This means that the range is [-2,∞)
Hence, the domain is (-∞,∞) and the range is [-2,∞)
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For her job, natasha spent a total of n minutes processing id card applications and driver's license applications. it takes natasha 15 minutes to process and id card aplication and 20 minutes to process a driver's license application. what is the value of n
Step-by-step explanation:
if I understand the question, write an equation for n in terms of i for number of Id cards an d for number driver license.
n = 15i + 20d
The value of n for a total minutes processing id card applications and driver's license applications would be 35 minutes.
Used the concept of addition that states,
The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.
Given that,
For her job, Natasha spent a total of n minutes processing id card applications and driver's license applications.
And, it takes Natasha 15 minutes to process an id card application and 20 minutes to process a driver's license application.
Now by the given condition, we get;
n = 15 minutes + 20 minutes
n = 35 minutes
Therefore, the value n is 35 minutes.
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Two planes that do not intersect are _____ parallel.
sometimes always never
Two planes that do not intersect are always parallel.
Solve x/3 = x+2/2. X=
Answer:
I will assume that the term "x+2/2" is meant to be "(x + 2)/2)." Otherwise the equation would read (x/3) = x + 1
Step-by-step explanation:
(x/3) = (x + 2)/2
x = 3*(x+2)/2 [Multiply both sides by 3]
x = (3x + 6)/2
x = (3/2)x + 6/2
x - (3/2)x = 3
-0.5x = 3
x = -6
====================
Check:
Does (x/3) = (x + 2)/2 for x = -6?
(-6/3) = (-6 + 2)/2
-2 = -4/2
-2 = -2 YES
