Question

graph the inequality on a number line.

1. ( r leq -9 )
2. ( g > 2.75 )
3. ( x geq -3\frac{1}{2} )
4. ( z < 1\frac{1}{4} )

Explanation:

Step1: Analyze \( r \leq -9 \)

To graph \( r \leq -9 \) on a number line:

• Find -9 on the number line.
• Since the inequality is "less than or equal to", we use a closed circle at -9 (to include -9) and shade to the left (for all values less than -9).

Step2: Analyze \( g > 2.75 \)

For \( g > 2.75 \):

• Locate 2.75 on the number line.
• The inequality is "greater than", so we use an open circle at 2.75 (to exclude 2.75) and shade to the right (for all values greater than 2.75).

Step3: Analyze \( x \geq -3\frac{1}{2} \) (or \( x \geq -\frac{7}{2} = -3.5 \))

For \( x \geq -3.5 \):

• Find -3.5 on the number line.
• The inequality is "greater than or equal to", so we use a closed circle at -3.5 and shade to the right.

Step4: Analyze \( z < 1\frac{1}{4} \) (or \( z < \frac{5}{4} = 1.25 \))

For \( z < 1.25 \):

• Locate 1.25 on the number line.
• The inequality is "less than", so we use an open circle at 1.25 and shade to the left.

Answer:

1. Closed circle at -9, shade left.
2. Open circle at 2.75, shade right.
3. Closed circle at -3.5, shade right.
4. Open circle at 1.25, shade left.