Question

Which of the following values of x satisfy the inequality 0.5x−0.75≥3.25?

a) x>8
b) x≥8
c) x<8
d) x≤8

Answer 1

To solve the inequality 0.5x - 0.75 ≥ 3.25, we add 0.75 to both sides and then divide by 0.5, resulting in x ≥ 8. The correct answer is b) x ≥ 8.

Step-by-step explanation:

To determine which values of x satisfy the inequality 0.5x - 0.75 ≥ 3.25, we need to solve the inequality by isolating x on one side:

• Add 0.75 to both sides of the inequality: 0.5x ≥ 4.00.
• Divide both sides by 0.5 to solve for x: x ≥ 8.

The solution to the inequality tells us that x must be greater than or equal to 8 to satisfy the original inequality. Therefore, the correct answer is b) x ≥ 8.

To solve the inequality 0.5x - 0.75 ≥ 3.25, you need to isolate the variable x.

1. Add 0.75 to both sides of the inequality: 0.5x ≥ 3.25 + 0.75. This simplifies to 0.5x ≥ 4.

2. Divide both sides of the inequality by 0.5: x ≥ 4 / 0.5. This simplifies to x ≥ 8.

So, the values of x that satisfy the inequality 0.5x - 0.75 ≥ 3.25 are x ≥ 8. Therefore, the correct answer is a) x > 8.