The given expression is
[tex]5|3x-9|+6\leq36[/tex]First, we isolate the absolute value
[tex]\begin{gathered} 5|3x-9|\leq36-6 \\ 5|3x-9|\leq30 \\ |3x-9|\leq\frac{30}{5} \\ |3x-9|\leq6 \end{gathered}[/tex]Now, we rewrite the inequality as two because the inequality has "less than or equal to".
[tex]3x-9\leq6,or,3x-9\ge-6[/tex]Let's solve each inequality
[tex]\begin{gathered} 3x-9\leq6 \\ 3x\leq6+9 \\ 3x\leq15 \\ x\leq\frac{15}{3} \\ x\leq5 \end{gathered}[/tex][tex]\begin{gathered} 3x-9\ge-6 \\ 3x\ge-6+9 \\ 3x\ge3 \\ x\ge\frac{3}{3} \\ x\ge1 \end{gathered}[/tex]The image below shows the solution set
