Example Question - solving absolute value equations

Solving Absolute Value Equations

The equation provided in the image is |2x - 3|^2 = 16. To solve for x, we need to take the square root of both sides of the equation and then solve the resulting absolute value equation. Starting with the equation: |2x - 3|^2 = 16 Take the square root of both sides to eliminate the square on the left side: |2x - 3| = √16 Since the square root of 16 is 4, we have: |2x - 3| = 4 The absolute value equation |2x - 3| = 4 can split into two possible equations because the absolute value of a number can be both positive and negative: 2x - 3 = 4 or 2x - 3 = -4 For the first equation: 2x - 3 = 4 2x = 7 x = 7/2 x = 3.5 For the second equation: 2x - 3 = -4 2x = -1 x = -1/2 x = -0.5 Therefore, there are two possible values for x: 3.5 and -0.5.