Question

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

Piecewise-Defined Functions
ANSWERED
asked 2021-02-21

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

Answers (1)

2021-02-22

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

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