Question

Solve the equation. $$|x+5|=6.5$$

Short answer

The solutions are \(x = 1.5\) and \(x = -11.5\).

Step-by-step solution

Create two Separate Equations

Since \(|x+5|=6.5\) has an absolute value, split it into two separate equations: \(x+5 = 6.5\) and \(x+5 = -6.5\).

Solve the first equation

Subtract 5 from both sides of the equation \(x+5=6.5\) to isolate \(x\). This gives us \(x = 6.5 - 5\) which simplifies to \(x = 1.5\).

Solve the second equation

Subtract 5 from both sides of the equation \(x+5=-6.5\) to isolate \(x\). This gives us \(x = -6.5 - 5\) which simplifies to \(x = -11.5\).