Solving Inequalities

Solve the inequality: 2x + 5 > 10

• x > 2.5

• x > 7.5

• x = 2.5

• x < 2.5

Answer explanation

To solve the inequality 2x + 5 > 10, first subtract 5 from both sides to get 2x > 5. Then, divide both sides by 2 to isolate x, resulting in x > 2.5. Therefore, the correct choice is x > 2.5.

Tags

CCSS.7.EE.B.4B

Solve the inequality: 3x - 7 < 4

• x > 11/3

• x > 4

• x < 7/3

• x < 11/3

Answer explanation

To solve the inequality 3x - 7 < 4, first add 7 to both sides, resulting in 3x < 11. Then, divide both sides by 3, which gives x < 11/3. Therefore, the correct choice is x < 11/3.

Tags

CCSS.7.EE.B.4B

Solve the inequality: -4x + 8 ≥ 20

• x < -3

• x > -3

• x ≥ -3

• x ≤ -3

Answer explanation

To solve the inequality -4x + 8 ≥ 20, first subtract 8 from both sides to get -4x ≥ 12. Then, divide both sides by -4. Remember to reverse the inequality sign when dividing by a negative number. So, x ≤ -3 is the correct choice.

Tags

CCSS.7.EE.B.4B

Solve the inequality: 2(x - 3) ≤ 10

• x ≤ 8

• x ≤ 5

• x > 8

• x ≥ 12

Answer explanation

To solve the inequality 2(x - 3) ≤ 10, first distribute the 2: 2x - 6 ≤ 10. Next, add 6 to both sides: 2x ≤ 16. Finally, divide by 2: x ≤ 8. Therefore, the correct choice is x ≤ 8.

Tags

CCSS.7.EE.B.4B

Solve the inequality: 5 - 3x > 7

• x < -2/3

• x > 2/3

• x < 2/3

• x > -2/3

Answer explanation

To solve the inequality 5 - 3x > 7, first subtract 5 from both sides to get -3x > 2. Then, divide both sides by -3. Since we're dividing by a negative number, we must reverse the inequality sign, resulting in x < -2/3. Therefore, the correct choice is x < -2/3.

Tags

CCSS.7.EE.B.4B

Solve the inequality: 2x + 3 > 5x - 2

• x > 5/3

• x < 5/3

• x < 3/5

• x > 3/5

Answer explanation

To solve the inequality 2x + 3 > 5x - 2, first subtract 2x from both sides to get 3 > 3x - 2. Then, add 2 to both sides to obtain 5 > 3x. Finally, divide both sides by 3 to find x < 5/3, which is the correct choice.

Solve the inequality: 4(x + 2) - 3 > 5(x - 1)

• x > -10

• x < -10

• x < 10

• x > 10

Answer explanation

To solve the inequality 4(x + 2) - 3 > 5(x - 1), first distribute the 4 and 5, then simplify the equation: 4x + 8 - 3 > 5x - 5. Combine like terms: 4x + 5 > 5x - 5. Subtract 4x from both sides: 5 > x - 5. Add 5 to both sides: x < 10. So, the correct choice is x < 10.

Solve the inequality: 2(3x - 1) + 4 < 5(2x + 3) - 1

• x < -3

• x = -3

• x > 3

• x > -3

Answer explanation

To solve the inequality 2(3x - 1) + 4 < 5(2x + 3) - 1, first distribute the numbers and simplify the equation. After combining like terms, you'll get -x < 8. Finally, divide by -1 and reverse the inequality sign, resulting in x > -3, which is the correct choice.

Solve the inequality: 3(x - 4) + 2 > 2(x + 1) - 5

• x > 7

• x < 7

• x > 8

• x > 6

Answer explanation

To solve the inequality 3(x - 4) + 2 > 2(x + 1) - 5, first distribute the 3 and 2: 3x - 12 + 2 > 2x + 2 - 5. Simplify both sides: 3x - 10 > 2x - 3. Subtract 2x from both sides: x - 10 > -3. Add 10 to both sides: x > 7. So, the correct choice is x > 7.

Solve the inequality: 2(x + 3) - 4 ≤ 3(x - 2) + 1

• x ≤ 7

• x > 7

• x ≤ 6

• x ≥ 7

Answer explanation

To solve the inequality, first distribute the 2 on the left side: 2x + 6 - 4 ≤ 3x - 6 + 1. Simplify both sides: 2x + 2 ≤ 3x - 5. Subtract 2x from both sides: 2 ≤ x - 5. Add 5 to both sides: x ≥ 7. Therefore, the correct choice is x ≥ 7.