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
\(\displaystyle{5}-{9}{<}{x}-{5}+{5}{<}{9}+{5}\)
\(\displaystyle-{4}{<}{x}{<}{13}\)
\(\displaystyle\therefore{x}\in{\left(-{4},{13}\right)}\)
Question
Find the value of x that satisfies the inequality.|x-5|<9
Answers (1)
2021-02-22
Relevant Questions
asked 2020-11-12
Find the value of x that satisfies the inequality.
\(\displaystyle{\left|{\frac{{{3}{x}+{1}}}{{{2}}}}\right|}{<}{1}\)
asked 2021-02-12
Solve the absolute value inequality \(\displaystyle{2}{\left|{3}{x}+{9}\right|}{<}{36}\).
asked 2021-01-04
Express the interval (0, 8) in terms of an inequality involving absolute value. (Use the variable x to describe the interval.)
asked 2021-01-27
Step 1
Solve absolute value inequality.
\(\displaystyle-{4}{\left|{{1}-{x}}\right|}{<}-{16}\)
