Question

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

Answer 1

Solution:

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)

$\begin{gathered} \frac{-3x}{-3}<\frac{15}{-3} \\ x>-5 \end{gathered}$

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)

$\begin{gathered} \frac{-3x}{-3}>\frac{-9}{-3} \\ x<3 \end{gathered}$

Hence,

The graph of the inequality will be