Calculate: |2x-7|=1

Expression: $|2x-7|=1$

Use the absolute value definition to rewrite the absolute value equation as two separate equations

$\begin{array} { l }2x-7=1,\\2x-7=-1\end{array}$

Solve the equation for $x$

$\begin{array} { l }x=4,\\2x-7=-1\end{array}$

Solve the equation for $x$

$\begin{array} { l }x=4,\\x=3\end{array}$

The equation has $2$ solutions

$\begin{array} { l }x_1=3,& x_2=4\end{array}$