Question

in exercises 29 - 36, graph the inequality. (see example 3.) 29. $xgeq2$ 30. $zleq5$ 31. $- 1>t$ 32. $-2 < w$ 33. $vleq - 4$ 34. $s < 1$ 35. $\frac{1}{4}

Explanation:

Step1: Identify the type of inequality

For $x\geq2$, it is a one - variable linear inequality.

Step2: Determine the boundary point

The boundary point is $x = 2$. Since the inequality is $\geq$, the boundary point is included in the solution set, so we use a closed - circle at $x = 2$ on the number line.

Step3: Determine the direction of the solution set

The inequality $x\geq2$ means all values of $x$ that are greater than or equal to 2. So we draw an arrow to the right of $x = 2$ on the number line.

For $z\leq5$, the boundary point is $z = 5$. Since the inequality is $\leq$, we use a closed - circle at $z = 5$ on the number line and draw an arrow to the left of $z = 5$ as it represents all values of $z$ less than or equal to 5.

For $-1>t$ (which is equivalent to $t < - 1$), the boundary point is $t=-1$. Since the inequality is $<$, we use an open - circle at $t = - 1$ on the number line and draw an arrow to the left of $t=-1$.

For $-2 < w$, the boundary point is $w=-2$. Since the inequality is $>$, we use an open - circle at $w = - 2$ on the number line and draw an arrow to the right of $w=-2$.

For $v\leq - 4$, the boundary point is $v=-4$. Since the inequality is $\leq$, we use a closed - circle at $v = - 4$ on the number line and draw an arrow to the left of $v=-4$.

For $s < 1$, the boundary point is $s = 1$. Since the inequality is $<$, we use an open - circle at $s = 1$ on the number line and draw an arrow to the left of $s = 1$.

For $\frac{1}{4}\frac{1}{4}$), the boundary point is $p=\frac{1}{4}$. Since the inequality is $>$, we use an open - circle at $p=\frac{1}{4}$ on the number line and draw an arrow to the right of $p=\frac{1}{4}$.

For $r\geq-\vert5\vert=- 5$, the boundary point is $r=-5$. Since the inequality is $\geq$, we use a closed - circle at $r=-5$ on the number line and draw an arrow to the right of $r=-5$.

Answer:

To graph $x\geq2$: Closed - circle at $x = 2$, arrow to the right.
To graph $z\leq5$: Closed - circle at $z = 5$, arrow to the left.
To graph $-1>t$: Open - circle at $t=-1$, arrow to the left.
To graph $-2 < w$: Open - circle at $w=-2$, arrow to the right.
To graph $v\leq - 4$: Closed - circle at $v=-4$, arrow to the left.
To graph $s < 1$: Open - circle at $s = 1$, arrow to the left.
To graph $\frac{1}{4}To graph $r\geq - 5$: Closed - circle at $r=-5$, arrow to the right.