Question

Solve and graph. |3 – v| < 6 Write the inequality as two inequalities without absolute value. Solve the inequality and write the solution set. Graph the solution on a number line.

Answer 1

`-3<v<9`

Explanation:

The inequality
`|3-v| < 6` is equivalent to the system of two inequalities:

`\left\{\begin{array}{l}3-v>-6\\ \\3-v<6\end{array}\right.`

Solve each inequality:

1.
`3-v>-6:`

`3-v>-6\\ \\-v>-6-3\\ \\-v>-9\\ \\v<9`

2.
`3-v<6:`

`-v<6-3\\ \\-v<3\\ \\v>-3`

The solution set to the initial inequality is

`-3<v<9`

The graph of this solution set is attached.