Question

Solve the equation. \(|x-5|=7\)

Short answer

The solutions to the equation \(|x-5|=7\) are \(x = -2\) and \(x = 12\).

Step-by-step solution

Solve for the case \(x-5 = 7\)

For the first case, in which \(x-5 = 7\), add 5 to both sides to solve for x. Doing so gives us: \(x = 7 + 5 = 12\)

Solve for the case \(x-5 = -7\)

For the second case, in which \(x-5 = -7\), again add 5 to both sides to solve for x. Doing this gives us: \(x = -7 + 5 = -2\)

Present the solution as a set

These two solutions can be collected into a set. So the solution set for the equation is: \{ -2, 12 \}