Question

Solve the equation. $$|x-3.2|=7$$

Short answer

The solutions of the equation \(|x-3.2|=7\) are \(x = 10.2\) and \(x = -3.8\).

Step-by-step solution

Split the Equation into two

The equation can be split into two separate cases due to the absolute value. This results into two equations: 1) \(x - 3.2 = 7\) and 2) \(x - 3.2 = -7\).

Solve the First Equation

To solve the first equation \(x - 3.2 = 7\), add 3.2 on both sides to isolate \(x\). This results in \(x = 7 + 3.2 = 10.2.\)

Solve the Second Equation

To solve the second equation \(x - 3.2 = -7\), add 3.2 on both sides to isolate \(x\). This results in \(x = -7 + 3.2 = -3.8.\)