Question

Solve the graph the absolute value inequality. See the picture. TY

Answer 1

We want to find the interval that satisfy the following inequality:

`|4x+1|\leq5`

Since we're dealing with an absolute value, we need to divide this problem in two cases.

The first case: If x > 0:

`\begin{gathered} 4x+1\leq5 \\ 4x\leq4 \\ x\leq1 \end{gathered}`

The second case: If x < 0:

`\begin{gathered} -(4x+1)\leq5 \\ -4x-1\leq5 \\ -4x\leq6 \\ x\ge-(3)/(2) \\ x\ge-1.5 \end{gathered}`

From this, we have our interval.

`-1.5\leq x\leq1`

The answer that fits this interval is the fourth option.