Question

solve each inequality. then, graph the solution on a number line.

1. ( s > - 4 )
2. ( t - 3 < - 6 )
3. ( 4 m > - 16 )
4. ( \frac { a } { - 4 } + 7 geq 2 )

Explanation:

1. Solve \(s > - 4\)

This inequality is already solved. To graph it, we draw an open circle at \(-4\) (because \(-4\) is not included in the solution set) and draw an arrow to the right.

2. Solve \(t - 3 < - 6\)

Step1: Add \(3\) to both sides

\(t-3 + 3< - 6+3\)
\(t<-3\)
To graph it, we draw an open circle at \(-3\) (because \(-3\) is not included in the solution set) and draw an arrow to the left.

3. Solve \(4m>-16\)

Step1: Divide both sides by \(4\)

\(\frac{4m}{4}>\frac{-16}{4}\)
\(m > - 4\)
To graph it, we draw an open circle at \(-4\) (because \(-4\) is not included in the solution set) and draw an arrow to the right.

4. Solve \(\frac{a}{-4}+7\geq2\)

Step1: Subtract \(7\) from both sides

\(\frac{a}{-4}+7 - 7\geq2 - 7\)
\(\frac{a}{-4}\geq - 5\)

Step2: Multiply both sides by \(-4\) (and reverse the inequality sign)

\(a\leq20\)
To graph it, we draw a closed circle at \(20\) (because \(20\) is included in the solution set) and draw an arrow to the left.

Answer:

1. \(s > - 4\), graph: open circle at \(-4\), arrow to the right.
2. \(t < - 3\), graph: open circle at \(-3\), arrow to the left.
3. \(m > - 4\), graph: open circle at \(-4\), arrow to the right.
4. \(a\leq20\), graph: closed circle at \(20\), arrow to the left.