Question

graphing an inequality graph the inequality on a number line.

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

Explanation:

Step1: Graph $r \leq -9$

1. Locate $-9$ on the number line.
2. Draw a closed circle at $-9$ (since the inequality includes equality, $\leq$).
3. Shade all numbers to the left of $-9$ (since $r$ is less than or equal to $-9$).

Step2: Graph $g > 2.75$

1. Locate $2.75$ on the number line.
2. Draw an open circle at $2.75$ (since the inequality does not include equality, $>$).
3. Shade all numbers to the right of $2.75$ (since $g$ is greater than $2.75$).

Step3: Graph $x \geq -3\frac{1}{2}$

1. Convert $-3\frac{1}{2}$ to $-3.5$ and locate it on the number line.
2. Draw a closed circle at $-3.5$ (since the inequality includes equality, $\geq$).
3. Shade all numbers to the right of $-3.5$ (since $x$ is greater than or equal to $-3.5$).

Step4: Graph $1\frac{1}{4} > z$ (rewrite as $z < 1.25$)

1. Convert $1\frac{1}{4}$ to $1.25$ and locate it on the number line.
2. Draw an open circle at $1.25$ (since the inequality does not include equality, $<$).
3. Shade all numbers to the left of $1.25$ (since $z$ is less than $1.25$).

Answer:

1. For $r \leq -9$: Closed circle at $-9$, shade left.
2. For $g > 2.75$: Open circle at $2.75$, shade right.
3. For $x \geq -3\frac{1}{2}$: Closed circle at $-3.5$, shade right.
4. For $1\frac{1}{4} > z$: Open circle at $1.25$, shade left.