Question

example 2 (page 118)
solve each inequality. graph the solution.

1. $4h < 16$
2. $3p > 36$
3. $9n \leq -27$
4. $6x < -48$
5. $-8b \geq -24$
6. $-5w \leq 30$
7. $-2t > 10$
8. $-10d \geq -70$

example 3 (page 118)

1. $\frac{p}{5} < -3$
2. $\frac{k}{4} \geq 6$
3. $\frac{w}{7} \leq -3$
4. $\frac{y}{7} > -8$
5. $\frac{n}{-2} > -5$
6. $\frac{m}{-6} \leq 5$
7. $\frac{x}{10} < -4$
8. $\frac{c}{-5} \geq -2$

Explanation:

Let's solve inequality 11: \(-10d \geq -70\)

Step 1: Divide both sides by -10 (remember to reverse the inequality sign when dividing by a negative number)

To isolate \(d\), we divide both sides of the inequality \(-10d \geq -70\) by \(-10\). When we divide or multiply an inequality by a negative number, the direction of the inequality sign changes. So we have:

$$ \frac{-10d}{-10} \leq \frac{-70}{-10} $$

Step 2: Simplify both sides

Simplifying the left side, \(\frac{-10d}{-10} = d\). Simplifying the right side, \(\frac{-70}{-10} = 7\). So we get:

$$ d \leq 7 $$

Answer:

The solution to the inequality \(-10d \geq -70\) is \(d \leq 7\). To graph this, we draw a number line, put a closed circle at 7 (because the inequality is "less than or equal to"), and shade to the left of 7 to represent all numbers less than or equal to 7.