Explain the process of solving inequality with variables on both sides. Show an example.

Answers

Answer 1

Answer:

Inequalities work exactly like equations with one exception. The process begins just like equations: first, do the opposite of what you see, then do the same thing on the other side of the sign. At the last step of solving an inequality, if you multiply or divide by a negative number, then you reverse the sign

Answer 2

The two examples show the process of solving inequality with variables on both sides are

3 + x > 3x - 6

3 - 4x < 2x + 8

The process is shown below.

What is inequality?

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal =

Greater than and equal=

We have,

Let us consider an inequality:

3 + x > 3x - 6 ____(1)
3 - 4x < 2x + 8 _____(2)

We will solve for x.

From (1),

3 + x > 3x - 6

Subtract 3 on both sides.

3 + x - 3 > 3x - 6 - 3

x > 3x - 9

Add 9 on both sides.

x + 9 > 3x - 9 + 9

x + 9 > 3x

Subtract x on both sides.

x + 9 - x > 3x - x

9 > 2x

Divide 2 on both sides.

9/2 > x

x < 9/2

This means that x must be less than 9/2.

From (2),

3 - 4x < 2x + 8

Subtract 3 on both sides.

3 - 4x - 3 < 2x + 8 - 3

- 4x < 2x + 5

Subtract -2x on both sides.

-4x - 2x < 2x + 5 - 2x

-6x < 5

Divide both sides by 6.

-x < 5/6

Since we can not keep a negative sign with x we will multiply a negative on both sides and flip the inequality.

- (-x) > -5/6

x > -5/6

Thus,

The two examples show the process of solving inequality with variables on both sides are:

3 + x > 3x - 6

= x < 9/2


3 - 4x < 2x + 8

= x > -5/6

Learn more about inequalities here:

https://brainly.com/question/20383699

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Related Questions

(03.05 MC) EXPLAIN PLZ
Sophia works in a clothing store and earns $40 per day. She earns an extra $5 for each outfit she sells. If Sophia wants to earn at least $70 per day, which inequality shows the minimum number of outfits, n, that she should sell? (5 points)

Select one:
a. 40 + 5n ≤ 70, so n ≤ 6
b. 40 + 5n ≥ 70, so n ≥ 25
c. 40 + 5n ≤ 70, so n ≤ 25
d. 40 + 5n ≥ 70, so n ≥ 6

Answers

Answer:

I think the answer is B.

Step-by-step explanation:

I am very sorry if it is incorrect.

Someone help me with this ASAP

Answers

Answer:

Image 1 - 5, 4, 4 Image 2 - -0.73, -21.93, 7.67 Image 3 - You can't carry more than 9 5/9 pounds of sugar onto the airplane. You have 9 2/3 pounds of sugar, will you be able to go onto the airplane?

Step-by-step explanation:

Answer:

ummmm......

Step-by-step explanation:

Which of the following equations is equivalent to 5(2p – 6) = 40?
A.10p – 30 = 40
B.7p – 11 = 40
C.7p – 1 = 40

Answers

Answer:

The correct answer is A. Can I have brainlest if I am right?

Step-by-step explanation:

Step-by-step explanation:

5(2p-6)=40

5×2=10,5×6=30

10+30=40

Please help!! I would really appreciate it.

Answers

Answer:

Bob cycled faster and the unit rate for Sam is 9mph

Step-by-step explanation:

Explanation - Bobby cycles 10 miles and hour/Sam cycles 9 miles an hours

Answer - Bobby cycles faster and the unit rate for Sam is 9/1 or 9 over 1

Tanya wants to earn enough money to buy a new Tigers shirt. So far she has earned $20, which is 50% of the money she needs to buy the shirt. How much does the shirt cost?

(Hint: It may be useful to draw a picture.)

The shirt costs ?
dollars.

Answers

The shirt would cost a total of $ 40

Answer:

I think the shirt cost 40 dollars cause 50% of 40 is 20

Step-by-step explanation:

Which of the following inequalities is equivalent to 1 ≥ x?

x ≥ 1
x ≤ -1
x ≥ -1
x ≤ 1

Answers

x< 1 with _ under the < sign

Answer:

x ≤ 1

Step-by-step explanation:

If you flip x with 1 and flip the sign you get x ≤ 1.

Please help me answer this

Answers

Answer:

The answer is c

Step-by-step explanation:

This answer is C rididofkepdpdppd

can you guys do this and show work so i can copy it? ill give you brainliest and point :

Answers

Don’t mind the mistake I made. The answers are right and the work is correct.

2) Which statement is correct?
[ Select ]

a) Perfect squares can be found by multiplying a number by itself.

b) Perfect squares can be found by multiplying a number by 2.

Answers

Answer:

a)

Step-by-step explanation:

Numbers should not be at the beginning or end of a sentence.

Option A is the right one

Help plz ............

Answers

Answer:

i think it is B.

Step-by-step explanation:

Pretty sure the right answer would be B

I need help with this ASAP!!!

Answers

Answer:

5.-2<x  

3.x-2 <0

2. 2<x

1.x<-2

4.x>2

Step-by-step explanation:

i think it could be sum else

Answer:

Step-by-step explanation:

-2x

Help!!!
Mr. Lombardo took his children to a water. He used the coupon shown below to buy one adult ticket. (This coupon is good for ONE adult ticket to World Of Water at a price of $28.00. YOU SAVE $4.00!) The price of admission for all three family members was $76. What was the price of each child's ticket?
Answer the following questions and explain your answer.
a. What ticket price do you know? How much is that ticket? Explian.
b. What other information is given in the problem?
c. How can you find the price of the two children's tickets? Show how to find the answer.
d. If you know the price of two children's tickets, how can you find the price of one child's ticket.
e. What is the price of each child's ticket? Show your work.

Answers

A. The price would be 24 because 28-4 dollars is 24
B. How much a cost altogether and the fact that he has two kids
C. You can take the total of the price of all their tickets combined subtract 24 and you would get 52 so so I slice and a half in and you have the answer
D 26 dollars each
E. 76-24=52 52/2=26

there are 200 freshmen in a high school. 30% of them take history. how many freshmen are enrolled in Spanish?

Answers

pretty sure it’s 140

3 part question

DIRECTIONS: Find the first 5 terms and the term requested. I wrote it in a word doc to you can see it better. plz dont answer if you dont know it. Its algebra 1 level work. Its arithmetic sequences. plz i need it ill give brainliest to the first person with correct answers.

Answers

Answer:

HI

Step-by-step explanation:

Please! I need help ASAP!

Answers

Answer:

need the answer still ?

Step-by-step explanation:

what are the slope and the y-intercept of the liner function that is represented by the equation y equals 9x - 2 the slope is -2 and the y-intercept is 9 the slope is 2 and the y-intercept is 9 the slope is 9 and the y-intercept is -2 the the slope is 9 and the y-intercept is 2​

Answers

Just a little help.

Hi there! I may not answer the other question But I certainly help you with what a slope is, see how a slope works are. Pick two points on the line and determine their coordinates. Hope this helps.

If you pick two points on a line and subtract left to right you can find your slope

-7/33 x (-11/7) PLEASE ANSWER ASAP >_

Answers

Answer:

3

Step-by-step explanation:

Cancel 77.

-\frac{1}{33}x\times -11−

​33

​1

​​ x×−11

2 Use this rule: \frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}

​b

​a

​​ ×

​d

​c

​​ =

​bd

​ac

​​ .

-\frac{1\times x\times -11}{33}−

​33

​1×x×−11

​​

3 Simplify  1\times x\times -111×x×−11  to  -11x−11x.

-\frac{-11x}{33}−

​33

​−11x

​​

4 Move the negative sign to the left.

-(-\frac{11x}{33})−(−

​33

​11x

​​ )

5 Simplify  \frac{11x}{33}

​33

​11x

​​   to  \frac{x}{3}

​3

​x

​​ .

-(-\frac{x}{3})−(−

​3

​x

​​ )

6 Remove parentheses.

\frac{x}{3}

​3

​x

​​

Answer:

11/33 x

Step-by-step explanation:

Find an equation with an x intercept of (-1, 0)

Answers

answer:

y=x+1 :)

step by step explanation:

2. slope help ASAP , thank you

Answers

slope: 5
yint: -3/1 :Dd

How the Right of Occupancy can be transferred or exchanged.

Answers

Answer:

I think the right occupancy would be like boat.

Step-by-step explanation:

The diagram shows parallel lines cut by two transversal lines creating a triangle. Which statements are true? Check all that apply.

1. ∠A and ∠G are alternate interior angles.

2. ∠A, ∠F, and ∠E form a straight line.

3. ∠H and ∠A are corresponding angles.

4. ∠E and ∠C are vertical angles.

5. m∠G = m∠E

6. m∠F = m∠C

Answers

Ignore the other answer, it's 2, 3, 5, 6.

Proof below:

please help will give BRAINLIEST BRAINLIEST BRAINLIEST BRAINLIEST BRAINLIEST BRAINLIEST BRAINLIEST BRAINLIEST BRAINLIEST BRAINLIEST BRAINLIEST BRAINLIEST for correct answer!!!!!!!!!!!!!

Answers

I believe the length of AD is 10.
the answer to this is 10

pls help my its now due in 20 minutes

Answers

Answer:

We can't see the equation to answer it

we can’t see the questions

good afternoon mates

Answers

Answer:

Afternoon has never been good tho...

Step-by-step explanation:

Can someone please help ? :(

Answers

Answer:

I'll list the answers as coordinates (just input the second number in each coordinate)

(-2, 11)

(0, 1)

(2, -9)

(4, -19)

Step-by-step explanation:

So you see how the x column is filled out? You plug in the numbers in each area and solve for y.

So we start off with -2. You take the x out and place -2 instead. Your equation should look like this:

y = -5 (-2) + 1

Next you multiply -5 and -2, giving you 10. Your equation would look like this now:

y = 10 + 1

Next you add 10 and 1 together, and you have your answer. Keep doing the same thing, but instead of -2 for x, use 0, 2, and 4.

Hope I helped! Have a nice day or night! ^-^

You plug all the numbers in for x and solve them
Y=-5(-2)+1 is 11
Y=-5(0)+1 is 1
Y=-5(2)+1 is -9
Y=-5(4)+1 Is-19

How many solutions does this equation have?

6q − 3 = 3 + 6q

Answers

Answer:

0 solutions

Step-by-step explanation:

[tex]6q-3=3+6q\qquad|\text{subtract }\ 6q\ \text{from both sides}\\\\6q-6q-3=3+6q-6q\\\\-3=3\qquad\bold{FALSE}\\\\\text{This equation has no solution}\ q\in\O[/tex]

A patio has an area of 286 square feet. If the length of the patio is 22 feet, what is the width?

Answers

The width is 13 ft I hope this helped you!

helppppppppppppppppp lol

Answers

Answer:

There are no solutions.

Step-by-step explanation:

If there is 74 and 54 but with the same 15x: there is no solution. Even with negative.

Answer:

There is no solutions

Step-by-step explanation:

lol

Which is an independent clause?

A. Their mother had sent them to Grandmother's home
B. because she could not care for them herself
C. After living in San Francisco for ten years
D. a place she had never seen before

Answers

The independent clause is A
A is the correct answer

PLZ ANSWER

If y=2x-3 what is the value of x when y=1

-1
1
-2
2

Answers

Answer:

first thing you gotta do is substitute x with -1 then you do the work first you gotta know your order of operation which is PEMDAS what that stands for is perentice exponent multiplication division addition and subtraction so then what you do first is 2*-1+3 2*-1=-2+3=1 and that is the answer you are WELCOME.

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

If y = 1

2x - 3 = 1

Which means 2x must be 4, because we know 4 - 3 = 1

so x must be 2, because the answer has to be something that makes 4 when we times it by 2.

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