Solving Inequalities One Variable

Pick the correct letter for:

6 > x

• A

• B

• C

• D

Jim has $8 to spend on pizza. The slice is $4 and each topping is $0.50. Create an inequality to represent the number of toppings Jim can get if he only buys one slice of pizza.

• 4x + 0.50 ≥ 8

• 0.50x + 4 < 8

• 0.50x +4 ≤ 8

• 4x +0.50 ≤ 8

Solve the inequality. Don't forget to check your solution set.
12 ≥ 15 - 6y

• y ≤ ½

• y ≤ 2

• y ≥ ½

• y ≥ 2

-3 − 6(4x + 6) > -111

• x > 3

• x < 3

• x < -3

• x > -3

5z - 2 - 2z < 13

• z > 5

• z < 5

• z > 1

• z < 1

Solve the inequality: 2x + 5 < 15

• x < 2

• x < 5

Answer explanation

To solve the inequality 2x + 5 < 15, subtract 5 from both sides to get 2x < 10. Then divide both sides by 2 to find x < 5. Therefore, the correct choice is x < 5.

Graph the solution set of the inequality: 3x - 4 ≥ 8

• x ≥ 4

• x = 8

Answer explanation

The solution set of the inequality 3x - 4 ≥ 8 is x ≥ 4. This is the correct choice because it represents all values of x that make the inequality true.

Find the solution to the inequality: 4x - 7 > 5

• x > 3

• x = 3

Answer explanation

To solve the inequality 4x - 7 > 5, we add 7 to both sides to isolate the variable. This gives us 4x > 12. Dividing both sides by 4, we find x > 3. Therefore, the correct choice is x > 3.

Graph the solution set of the inequality: 2x + 3 ≤ 9

• x ≤ 3

• x < 3

Answer explanation

The correct solution set for the inequality 2x + 3 ≤ 9 is x ≤ 3. This is because when we subtract 3 from both sides of the inequality, we get 2x ≤ 6. Dividing both sides by 2, we find x ≤ 3.

Solve the inequality: 6x + 2 < 20

• x = 3

• x < 3

Answer explanation

The correct choice is x < 3 because when we solve the inequality 6x + 2 < 20, we subtract 2 from both sides and divide by 6 to get x < 3.