Question

# Find the value of x that satisfies the inequality.|x-5|<9

Piecewise-Defined Functions

Find the value of x that satisfies the inequality.
$$\displaystyle{\left|{x}-{5}\right|}{<}{9}$$

2021-02-22

Solution:
$$\displaystyle{\left|{x}-{5}\right|}{<}{9}$$
set up compound inequality by removing the absolute value
$$\displaystyle-{9}{<}{x}-{5}{<}{9}$$
$$\displaystyle{5}-{9}{<}{x}-{5}+{5}{<}{9}+{5}$$
$$\displaystyle-{4}{<}{x}{<}{13}$$
$$\displaystyle\therefore{x}\in{\left(-{4},{13}\right)}$$