Question

1. graph: ( x > - 4 ) 6. circle each that is in the solution set for ( x > - 8 ) - 8 4 20/4 7 - 10 2. graph: ( x geq - 2.5 ) 7. circle each that is in the solution set for ( x leq 6 ) - 4.8 ( sqrt{16} ) 20/4 5.5 9 3. graph: ( 5 < x ) 8. circle each that is in the solution set for ( - 4 > x ) - 4.25 - 3 21/5 - 5.5 1 4. graph: ( 1/4 geq x ) 9. circle each that is in the solution set for ( 2 geq x ) 2 ( - sqrt{4} ) 10/5 1.95 13 5. graph: ( x < - 1 ) 10. circle each that is in the solution set for ( x leq 1/2 ) 3/4 ( sqrt{1} ) 13/26 2.5 1/4

Explanation:

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

• \(-8\) is not greater than \(-8\) (\(-8=-8\)).
• \(4\) (since \(\frac{20}{4} = 5\)), and \(5>-8\).
• \(7>-8\).
• \(-10<-8\).

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

• \(-4.8\leq5\).
• \(\sqrt{16}=4\leq5\).
• \(\frac{20}{4} = 5\leq5\).
• \(5.5>5\).
• \(9>5\).

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

• \(-4.25<-4\).
• \(-3>-4\).
• \(\frac{21}{5}=4.2>-4\).
• \(-5.5<-4\).
• \(1>-4\).

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

• \(2 = 2\).
• \(-\sqrt{4}=-2\leq2\).
• \(\frac{10}{5} = 2\leq2\).
• \(1.95\leq2\).
• \(13>2\).

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

• \(\frac{3}{4}=0.75>\frac{1}{2}\).
• \(\sqrt{1}=1>\frac{1}{2}\).
• \(\frac{13}{26}=\frac{1}{2}\leq\frac{1}{2}\).
• \(2.5>\frac{1}{2}\).
• \(\frac{1}{4}\leq\frac{1}{2}\).

Answer:

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