Solve the absolute value equation. |−2x+5|=3

Question

Responses
x = -4 or x = 0
x = 1
x = 0
x = 1 or x = 4

Answer 1

To solve the absolute value equation |−2x+5|=3, we can set up two separate equations and solve for x.

First equation: −2x+5 = 3
Solving for x, we subtract 5 from both sides:
−2x = 3 - 5
−2x = -2
Dividing both sides by -2 gives us:
x = 1

Second equation: −2x+5 = -3
Solving for x, we subtract 5 from both sides:
−2x = -3 - 5
−2x = -8
Dividing both sides by -2 gives us:
x = 4

Therefore, the solutions to the absolute value equation |−2x+5|=3 are x = 1 or x = 4.