Question

What is the solution set in inequality notation for the equation ∣2x−5∣=4? Select the correct option:

A. x ≤ 9/2 or x ≥ 13/2
B. x ≤ 1/2 or x ≥ 4
C. x ≤ 3/2 or x ≥ 4
D. x ≤ 9/2 or x ≥ 4

Answer 1

To find the solution set in inequality notation for the equation |2x−5|=4, isolate the absolute value expression and solve for x. The solution is x ≤ 9/2 or x ≥ 1/2.

Step-by-step explanation:

To find the solution set in inequality notation for the equation |2x−5|=4, we need to isolate the absolute value expression and solve for x. Here are the steps:

1. Write two separate equations without the absolute value: 2x-5 = 4 and 2x-5 = -4
2. Solve each equation for x: 2x = 9 and 2x = 1
3. Divide both sides by 2 to isolate x: x = 9/2 and x = 1/2
4. Write the solution set in inequality notation:

Solution: x ≤ 9/2 or x ≥ 1/2