Question

Solve the equation. \(|x+6|=13\)

Short answer

The solutions of the equation \(|x+6|=13\) are \(x=7\) and \(x=-19\).

Step-by-step solution

Understand the Properties of Absolute Value

The absolute value of a number is its distance from zero on the number line. It is always non-negative. It can be represented as either positive or negative. Thus, \(|x+6|=13\) is equivalent to \(x+6=13\) or \(x+6=-13\).

Solve for \(x\) in \(x+6=13\)

To solve for \(x\), subtract 6 from both sides of the equation to isolate \(x\). This gives \(x=13-6\), thus \(x=7\).

Solve for \(x\) in \(x+6=-13\)

Just like before, subtract 6 from both sides of the equation. This gives \(x=-13-6\), which simplifies to \(x=-19\).