Answer
The solution to the inequality is x > 22/3 or x < -32/3
Explanation
The given inequality is:
[tex]|x+\frac{5}{3}|-3>6[/tex]The inequality can be solved as follows:
[tex]\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}[/tex]Now, split the absolute value into two inequalities, for case > 9 or < -9
[tex]\begin{gathered} x+\frac{5}{3}>9\text{ }or\text{ }x+\frac{5}{3}<-9 \\ \\ x>9-\frac{5}{3}\text{ }or\text{ }x<-9-\frac{5}{3} \\ \\ x\gt\frac{27-5}{3}\text{ }or\text{ }x\lt\frac{-27-5}{3} \\ \\ x>\frac{22}{3}\text{ }or\text{ }x<\frac{-32}{3} \end{gathered}[/tex]Hence the solution to the inequality | x + 5/3 | -3 > 6 is x > 22/3 or x < -32/3
