Question

On separate sheet of paper Solve and graph 2 open vertical bar x minus 1 close vertical bar plus 3 less or equal than 9

Answer 1

Step-by-step explanation:

First, we solve the value/s of x to make a graph for the equation:

`2|x-1|+3\leq9`

So,we add -3 to both sides:

2|x-1|+3-3≤9-3

Simplify

2|x-1|≤6

`\begin{gathered} \text{Divide both sides by 2} \\ (2|x-1|)/(2)\leq(6)/(2) \\ \text{Simplify} \\ |x-1|\leq3 \end{gathered}`

Then, we apply the absolute rule: If |u|≤a, a>0 then -a≤u≤a.

`\begin{gathered} -3\leq x-1\leq3 \\ We\text{ add 1 to the whole equation to get the value of x} \\ -3+1\leq x-1+1\leq3+1 \\ \text{Simplify} \\ -2\leq x\leq4 \end{gathered}`

The values are:

x≤ 4 and x ≥ -2

Therefore, the graph is: