Question

Solve and graph each compound inequality.-3x + 4 < 19 and -3x + 4 > -5

Answer 1

The inequality is given below as

`-3x+4<19,-3x+4>-5`

Step 1:

Solve the first inequality given as

`-3x+4<19`

Subtract 4 from both sides

`\begin{gathered} -3x+4-4<19-4 \\ -3x<15 \end{gathered}`

Divide both sides by -5 (note: the inequality sign will be reversed)

`\begin{gathered} (-3x)/(-3)<(15)/(-3) \\ x>-5 \end{gathered}`

Hence,

The graph of the inequality will be

Step 2:

Solve the second inequality given as

`-3x+4>-5`

Subtract 4 from both sides

`\begin{gathered} -3x+4>-5 \\ -3x+4-4>-5-4 \\ -3x>-9 \end{gathered}`

Divide both sides by -3( note: the inequality sign will be reversed)

`\begin{gathered} (-3x)/(-3)>(-9)/(-3) \\ x<3 \end{gathered}`

Hence,

The graph of the inequality will be