Adding 1 to both sides gives
[tex]\frac{1}{3}|2x+3|\leq9[/tex]and then multiplying both sides by 3 gives
[tex]|2x+3|\leq27[/tex]At this point, this absolute value inequality can be decomposed into two separate inequalities
[tex]\begin{gathered} -(2x+3)<27 \\ (2x+3)<27 \end{gathered}[/tex]We first solve the first inequality.
Multiplying both sides by -1 reverses the sign of the inequality and gives
[tex]2x+3>-27[/tex]subtracting -3 from both sides we get
[tex]2x>-30[/tex]and finally dividing both sides by 2 gives
[tex]x>-15.[/tex]That is the first solution, the second solution is given by the second inequality 2x+ 3 <27.
Subtracting 3 from both sides and then dividing the equation by 2 gives
[tex]x<12[/tex]Hence, the solution to our inequality is
[tex]-15
