Question

Solve the equation. $$|x|=25$$

Short answer

The solutions to the equation are \(x\) = 25 and \(x\) = -25.

Step-by-step solution

Identify the absolute value

The absolute value equation is |x| = 25

Find the positive solution

First consider the case when the value inside the absolute value bars is positive. If \(x\) is positive, then \(x\) = 25 is a solution.

Find the negative solution

Next, consider the case when the value inside the absolute value bars is negative. This occurs when -\(x\) is positive, so -\(x\) = 25, and \(x\) = -25 is a solution.