# Multi Step Inequalities Quiz - By Melissa Barnhart

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| By Melissa Barnhart
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Melissa Barnhart
Community Contributor
Quizzes Created: 1 | Total Attempts: 282
Questions: 6 | Attempts: 282

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Solving Multi-Step Inequalities

• 1.

### Solve.  5(x - 2) > 20

• A.

X < 6

• B.

X > 2

• C.

X < 2

• D.

X > 6

D. X > 6
Explanation
The given inequality is 5(x - 2) > 20. To solve this, we first distribute 5 to both terms inside the parentheses, resulting in 5x - 10 > 20. Next, we add 10 to both sides to isolate the variable, which gives us 5x > 30. Finally, we divide both sides by 5 to solve for x, giving us x > 6.

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• 2.

### Solve.  -5p - 5 - 2p < -33

• A.

P > -4

• B.

P < 5.14

• C.

P > 4

• D.

P < 5

C. P > 4
Explanation
The given inequality is solved by combining like terms and isolating the variable p. By adding 5 to both sides and combining like terms, we get -7p - 5 < -33. Then, by adding 7p to both sides and subtracting 33 from both sides, we get -5 < 7p - 33. By adding 33 to both sides, we get 28 < 7p. Finally, by dividing both sides by 7, we get p > 4.

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• 3.

### Solve.  3(x + 2) - 4 < 92

• A.

X < -30

• B.

X < 30

• C.

X > 30

• D.

X > -30

B. X < 30
Explanation
To solve the inequality, we first distribute the 3 to both terms inside the parentheses: 3x + 6 - 4 < 92. Simplifying further, we have 3x + 2 < 92. Next, we subtract 2 from both sides of the inequality: 3x < 90. Finally, we divide both sides by 3 to isolate x: x < 30. Therefore, the correct answer is x < 30.

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• 4.

### Solve for x:4(x - 1) + 3 > 15

• A.

X > 4

• B.

X > -4

• C.

X < 4

• D.

X < -4

A. X > 4
Explanation
To solve the inequality 4(x - 1) + 3 > 15, we first distribute 4 to the terms inside the parentheses, resulting in 4x - 4 + 3 > 15. Simplifying further, we get 4x - 1 > 15. Adding 1 to both sides, we have 4x > 16. Finally, dividing both sides by 4, we find that x > 4. Therefore, the correct answer is x > 4.

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• 5.

### Solve for x:-10x + 6 + 8x ≤ 20

• A.

X ≤ -7

• B.

X ≥ -7

• C.

X ≥ 7

• D.

X ≤ 7

B. X ≥ -7
Explanation
The given inequality is solved by combining like terms and isolating the variable x. By subtracting 6 from both sides of the inequality, we get -10x + 8x ≤ 14. Simplifying further, we have -2x ≤ 14. Dividing both sides by -2, we find that x ≥ -7. Therefore, the answer is x ≥ -7.

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• 6.

### Which answer represents the graph above?

• A.

X > 3

• B.

X ≤ 3

• C.

X ≥ 3

C. X ≥ 3
Explanation
The graph above represents the solution set where x is greater than or equal to 3. This is because the line on the graph is solid and includes the point (3,0), indicating that 3 is included in the solution set. Therefore, the correct answer is x ≥ 3.

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