Solve the Absolute Value Equation: 2|x + 1| = 8

Question

Solve for x x in the equation 2x+1=8 2|x + 1| = 8 .

Step-by-Step Solution

Given the equation 2x+1=8 2|x + 1| = 8 , divide both sides by 2: x+1=4|x + 1| = 4.

Consider the two cases for the absolute value:

  1. Case 1: x+1=4x + 1 = 4
    Subtract 1: x=3x = 3.
  2. Case 2: x+1=4x + 1 = -4
    Subtract 1: x=5x = -5.

Thus, xx is 3 or 5 3 \text{ or } -5 .

Answer

x=3 or x=5 x = 3 \text{ or } x = -5