Question

Solve and give the answer as an interval.This is homework not exam

Answer 1

we have the inequality

`4\lvert2x-9\rvert-10\leq18`

Simplify the expression

`\begin{gathered} 4\lvert2x-9\rvert\leq18+10 \\ 4\lvert2x-9\rvert\leq28 \end{gathered}`
`\begin{gathered} \lvert2x-9\rvert\leq(28)/(4) \\ \lvert2x-9\rvert\leq7 \end{gathered}`

step 1

Find out the positive case

`\begin{gathered} +(2x-9)\leq7 \\ 2x\leq7+9 \\ 2x\leq11 \\ x\leq(11)/(2) \end{gathered}`

The solution of the positive case is the interval (-infinite,11/2]

step 2

Find out the negative case

`\begin{gathered} -(2x-9)\leq7 \\ (2x-9)\ge-7 \end{gathered}`
`\begin{gathered} 2x\ge-7+9 \\ 2x\ge2 \\ x\ge1 \end{gathered}`

The solution of the negative case is the interval [1,