## Intermediate Algebra (12th Edition)

$\left( 1,9 \right)$
Since for any $a\gt0$, $|x|\lt a$ implies $-a\lt x\lt a,$ then the given inequality, $|5-x|\lt4 ,$ is equivalent to \begin{array}{l}\require{cancel} -4\lt 5-x\lt4 .\end{array} Using the properties of inequality, then \begin{array}{l}\require{cancel} -4-5\lt 5-5-x\lt4-5 \\\\ -9\lt -x\lt-1 \\\\ 9\gt x\gt1 \\\\ 1\lt x\lt9 .\end{array} Hence, the solution is the interval $\left( 1,9 \right) .$