Question

Solve 12r - 11 - 354 and represent the solution set on a number line.

Answer 1

Solve the following inequality:

`\lvert2x-1\rvert-3\leq4`

As a first step we are going to add 3 to both sides:

`\begin{gathered} \lvert2x-1\rvert-3+3\leq4+3 \\ \lvert2x-1\rvert\leq7 \end{gathered}`

Then, we need to solve absolute value:

`\begin{gathered} \lvert2x-1\rvert\leq7 \\ We\text{ know 2x-1}\leq7\text{ and 2x-1}\ge-7 \end{gathered}`

Now, for the first inequality:

`\begin{gathered} 2x-1\leq7 \\ 2x-1+1\leq7+1 \\ 2x\leq8 \\ x\leq(8)/(2) \\ x\leq4 \end{gathered}`

For the second inequality:

`\begin{gathered} 2x-1\ge-7 \\ 2x-1+1\ge-7+1 \\ 2x\ge-6 \\ x\ge-(6)/(2) \\ x\ge-3 \end{gathered}`

The solution set would be, x≤4 and x≥−3, to represent on the number line: