Question

directions: answer each question below.

1. graph: ( x > - 4 )
2. graph: ( x geq - 2.5 )
3. graph: ( 5 < x )
4. graph: ( \frac { 1 } { 4 } geq x )
5. graph: ( x < - 1 )
6. circle each that is in the solution set for ( x > - 8 )

-8 1/4 ( \frac { 20 } { 4 } ) -7 -10

1. circle each that is in the solution set for ( x leq 5 )

-4.8 ( sqrt { 16 } ) ( \frac { 20 } { 4 } ) 5.5 9

1. circle each that is in the solution set for ( - 4 > x )

-4.25 -3 ( \frac { 21 } { 5 } ) -5.5 1

1. circle each that is in the solution set for ( 2 geq x )

2 ( - sqrt { 4 } ) ( \frac { 10 } { 5 } ) 1.95 13

1. circle each that is in the solution set for ( x leq \frac { 1 } { 2 } )

3/4 ( sqrt { 1 } ) ( \frac { 13 } { 26 } ) 2.5 1/4

Explanation:

Step1: Analyze each value for \(x > - 8\)

For \(x=-8\), since \(x > - 8\) does not include \(x = - 8\), so \(-8\) is not in the solution set.
For \(x=\frac{1}{4}\), \(\frac{1}{4}=-0.25>-8\), so \(\frac{1}{4}\) is in the solution set.
For \(x = \frac{20}{4}=5>-8\), so \(\frac{20}{4}\) is in the solution set.
For \(x=-7\), \(-7>-8\), so \(-7\) is in the solution set.
For \(x=-10\), \(-10<-8\), so \(-10\) is not in the solution set.

Step2: Analyze each value for \(x\leq5\)

For \(x=-4.8\), \(-4.8\leq5\), so \(-4.8\) is in the solution set.
For \(x=\sqrt{16} = 4\leq5\), so \(\sqrt{16}\) is in the solution set.
For \(x=\frac{20}{4}=5\), \(5 = 5\), so \(\frac{20}{4}\) is in the solution set.
For \(x = 5.5\), \(5.5>5\), so \(5.5\) is not in the solution set.
For \(x = 9\), \(9>5\), so \(9\) is not in the solution set.

Step3: Analyze each value for \(-4>x\)

For \(x=-4.25\), \(-4.25<-4\), so \(-4.25\) is in the solution set.
For \(x=-3\), \(-3>-4\), so \(-3\) is not in the solution set.
For \(x=\frac{21}{5}=4.2>-4\), so \(\frac{21}{5}\) is not in the solution set.
For \(x=-5.5\), \(-5.5<-4\), so \(-5.5\) is in the solution set.
For \(x = 1\), \(1>-4\), so \(1\) is not in the solution set.

Step4: Analyze each value for \(2\geq x\)

For \(x = 2\), \(2=2\), so \(2\) is in the solution set.
For \(x=-\sqrt{4}=-2\leq2\), so \(-\sqrt{4}\) is in the solution set.
For \(x=\frac{10}{5}=2\), \(2 = 2\), so \(\frac{10}{5}\) is in the solution set.
For \(x = 1.95\leq2\), so \(1.95\) is in the solution set.
For \(x = 13>2\), so \(13\) is not in the solution set.

Step5: Analyze each value for \(x\leq\frac{1}{2}\)

For \(x=\frac{3}{4}=0.75>\frac{1}{2}\), so \(\frac{3}{4}\) is not in the solution set.
For \(x=\sqrt{1}=1>\frac{1}{2}\), so \(\sqrt{1}\) is not in the solution set.
For \(x=\frac{13}{26}=\frac{1}{2}\), \(\frac{1}{2}=\frac{1}{2}\), so \(\frac{13}{26}\) is in the solution set.
For \(x = 2.5>\frac{1}{2}\), so \(2.5\) is not in the solution set.
For \(x=\frac{1}{4}=0.25\leq\frac{1}{2}\), so \(\frac{1}{4}\) is in the solution set.

Answer:

1. \(\frac{1}{4}\), \(\frac{20}{4}\), \(-7\)
2. \(-4.8\), \(\sqrt{16}\), \(\frac{20}{4}\)
3. \(-4.25\), \(-5.5\)
4. \(2\), \(-\sqrt{4}\), \(\frac{10}{5}\), \(1.95\)
5. \(\frac{13}{26}\), \(\frac{1}{4}\)