Multi Step Inequalities Quiz - By Melissa Barnhart

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

X > 4

X > -4

X < 4

X < -4

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.

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.

2. Solve. 5(x - 2) > 20

X < 6

X > 2

X < 2

X > 6

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.

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.

3. Solve. 3(x + 2) - 4 < 92

X < -30

X < 30

X > 30

X > -30

To solve the inequality, we first distribute the 3 to both terms inside the parentheses: 3x + 6 - 4

Explanation

To solve the inequality, we first distribute the 3 to both terms inside the parentheses: 3x + 6 - 4

4. Solve. -5p - 5 - 2p < -33

P > -4

P < 5.14

P > 4

P < 5

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 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 4.

5.

Which answer represents the graph above?

X > 3

X ≤ 3

X ≥ 3

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.

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.

6. Solve for x:-10x + 6 + 8x ≤ 20

X ≤ -7

X ≥ -7

X ≥ 7

X ≤ 7

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.

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.