Question

I need some help please out of the shift and I am going.

Answer 1

The given expression is

`5|3x-9|+6\leq36`

First, we isolate the absolute value

`\begin{gathered} 5|3x-9|\leq36-6 \\ 5|3x-9|\leq30 \\ |3x-9|\leq(30)/(5) \\ |3x-9|\leq6 \end{gathered}`

Now, we rewrite the inequality as two because the inequality has "less than or equal to".

`3x-9\leq6,or,3x-9\ge-6`

Let's solve each inequality

`\begin{gathered} 3x-9\leq6 \\ 3x\leq6+9 \\ 3x\leq15 \\ x\leq(15)/(3) \\ x\leq5 \end{gathered}`
`\begin{gathered} 3x-9\ge-6 \\ 3x\ge-6+9 \\ 3x\ge3 \\ x\ge(3)/(3) \\ x\ge1 \end{gathered}`

The image below shows the solution set