Question

in exercises 29 - 36, graph the inequality. (see example 3.)

1. $xgeq2$
2. $zleq5$
3. $-1 > t$
4. $-2 < w$
5. $vleq - 4$
6. $s < 1$
7. $\frac{1}{4}
8. $rgeq$

Explanation:

Step1: Recall graph - ing rules for inequalities

For \(x\geq a\), we draw a closed - circle at \(a\) on the number line and shade to the right. For \(x > a\), we draw an open - circle at \(a\) and shade to the right. For \(x\leq a\), we draw a closed - circle at \(a\) and shade to the left. For \(x < a\), we draw an open - circle at \(a\) and shade to the left.

Step2: Graph \(x\geq2\)

Draw a closed - circle at \(x = 2\) on the number line and shade all the values of \(x\) to the right of \(2\) including \(2\) itself.

Step3: Graph \(z\leq5\)

Draw a closed - circle at \(z = 5\) on the number line and shade all the values of \(z\) to the left of \(5\) including \(5\) itself.

Step4: Graph \(-1>t\) (or \(t < - 1\))

Draw an open - circle at \(t=-1\) on the number line and shade all the values of \(t\) to the left of \(-1\).

Step5: Graph \(-2 < w\) (or \(w>-2\))

Draw an open - circle at \(w = - 2\) on the number line and shade all the values of \(w\) to the right of \(-2\).

Step6: Graph \(v\leq - 4\)

Draw a closed - circle at \(v=-4\) on the number line and shade all the values of \(v\) to the left of \(-4\).

Step7: Graph \(s < 1\)

Draw an open - circle at \(s = 1\) on the number line and shade all the values of \(s\) to the left of \(1\).

Step8: Graph \(\frac{1}{4}\frac{1}{4}\))

Draw an open - circle at \(p=\frac{1}{4}\) on the number line and shade all the values of \(p\) to the right of \(\frac{1}{4}\).

Answer:

For \(x\geq2\): Closed - circle at \(2\), shade right. For \(z\leq5\): Closed - circle at \(5\), shade left. For \(-1>t\): Open - circle at \(-1\), shade left. For \(-2 < w\): Open - circle at \(-2\), shade right. For \(v\leq - 4\): Closed - circle at \(-4\), shade left. For \(s < 1\): Open - circle at \(1\), shade left. For \(\frac{1}{4}