we have the inequality
[tex]4\lvert2x-9\rvert-10\leq18[/tex]
Simplify the expression
[tex]\begin{gathered} 4\lvert2x-9\rvert\leq18+10 \\ 4\lvert2x-9\rvert\leq28 \end{gathered}[/tex][tex]\begin{gathered} \lvert2x-9\rvert\leq\frac{28}{4} \\ \lvert2x-9\rvert\leq7 \end{gathered}[/tex]
step 1
Find out the positive case
[tex]\begin{gathered} +(2x-9)\leq7 \\ 2x\leq7+9 \\ 2x\leq11 \\ x\leq\frac{11}{2} \end{gathered}[/tex]
The solution of the positive case is the interval (-infinite,11/2]
step 2
Find out the negative case
[tex]\begin{gathered} -(2x-9)\leq7 \\ (2x-9)\ge-7 \end{gathered}[/tex][tex]\begin{gathered} 2x\ge-7+9 \\ 2x\ge2 \\ x\ge1 \end{gathered}[/tex]
The solution of the negative case is the interval [1,
