Question

Solve the inequality | x + 5/3 | -3 > 6

Answer 1

Answer

The solution to the inequality is x > 22/3 or x < -32/3

Explanation

The given inequality is:

$|x+\frac{5}{3}|-3>6$

The inequality can be solved as follows:

$\begin{gathered} |x+\frac{5}{3}|-3>6 \\ \\ Take-3\text{ }to\text{ }the\text{ }other\text{ }side\text{ }of\text{ }the\text{ }inequality\text{ }sign \\ \\ |x+\frac{5}{3}|>6+3 \\ \\ |x+\frac{5}{3}|>9 \end{gathered}$

Now, split the absolute value into two inequalities, for case > 9 or < -9

$\begin{gathered} x+\frac{5}{3}>9\text{ }or\text{ }x+\frac{5}{3}9-\frac{5}{3}\text{ }or\text{ }x\frac{22}{3}\text{ }or\text{ }x$

Hence the solution to the inequality | x + 5/3 | -3 > 6 is x > 22/3 or x < -32/3