Question

practice

1. the minimum deposit for a new checking account is $75. write an inequality to represent the amounts in dollars $a$ that could be deposited in a new checking account. (example 1)
2. to win a medal in a 5k race, a runners time must be less than 22 minutes. write an inequality to represent the times in minutes $m$ that would win a medal. (example 1)

graph each inequality on the number line. (examples 2 and 3)

1. $b < -1.5$
2. $d \geq 4.75$
3. $a > \frac{4}{5}$
4. $d \leq -2\frac{1}{4}$
5. which of the following are solutions of the inequality $t + 7 \leq 12$: 4, 5, 6? (example 4)
6. which of the following are solutions of the inequality $h - 4 > 9$: 12, 13, 14? (example 4)
7. which of the following are solutions of the inequality $8r \geq 1.8$: $\frac{1}{5}$, $\frac{1}{4}$, $\frac{1}{3}$? (example 5)
8. which of the following are solutions of the inequality $\frac{2.4}{n} < 6$: 0.25, 0.4, 0.5? (example 5)
9. jessica has $32 to buy movie tickets that cost $5.25 each for her and her friends. the inequality $32 \geq 5.25t$ represents the number of tickets $t$ she could buy. what is the greatest number of tickets jessica can buy? (example 6)

test practice

1. multiselect stanley has $18 to spend on packs of trading cards that cost $1.50 each. the inequality $18 \geq 1.5p$ represents the number of packs $p$ he can buy. identify all the numbers of packs stanley can buy

10 packs
13 packs
11 packs
14 packs
12 packs
15 packs

Explanation:

Step1: Write min deposit inequality

$a \geq 75$

Step2: Write medal time inequality

$m < 22$

Step3: Graph $b < -1.5$

Draw an open circle at $-1.5$, shade left.

Step4: Graph $d \geq 4.75$

Draw a closed circle at $4.75$, shade right.

Step5: Graph $a > \frac{4}{5}$

Draw an open circle at $\frac{4}{5}$, shade right.

Step6: Graph $d \leq -2\frac{1}{4}$

Draw a closed circle at $-2\frac{1}{4}$, shade left.

Step7: Test $t+7 \leq 12$

For $t=4$: $4+7=11 \leq 12$ ✔️; $t=5$: $5+7=12 \leq 12$ ✔️; $t=6$: $6+7=13 > 12$ ❌

Step8: Test $h-4 > 9$

For $h=12$: $12-4=8
ot> 9$ ❌; $h=13$: $13-4=9
ot> 9$ ❌; $h=14$: $14-4=10 > 9$ ✔️

Step9: Test $8r \geq 1.8$

$r=\frac{1}{5}=0.2$: $8(0.2)=1.6 < 1.8$ ❌; $r=\frac{1}{4}=0.25$: $8(0.25)=2 \geq 1.8$ ✔️; $r=\frac{1}{3}\approx0.333$: $8(0.333)\approx2.664 \geq 1.8$ ✔️

Step10: Test $\frac{2.4}{n} < 6$

$n=0.25$: $\frac{2.4}{0.25}=9.6 > 6$ ❌; $n=0.4$: $\frac{2.4}{0.4}=6
ot< 6$ ❌; $n=0.5$: $\frac{2.4}{0.5}=4.8 < 6$ ✔️

Step11: Solve $32 \geq 5.25t$

$t \leq \frac{32}{5.25} \approx 6.095$, so $t=6$

Step12: Solve $18 \geq 1.5p$

$p \leq \frac{18}{1.5}=12$. Valid values: 10 packs, 11 packs, 12 packs

Answer:

1. $a \geq 75$
2. $m < 22$
3. Open circle at $-1.5$, shade left on the number line
4. Closed circle at $4.75$, shade right on the number line
5. Open circle at $\frac{4}{5}$, shade right on the number line
6. Closed circle at $-2\frac{1}{4}$, shade left on the number line
7. 4, 5
8. 14
9. $\frac{1}{4}$, $\frac{1}{3}$
10. 0.5
11. 6
12. 10 packs, 11 packs, 12 packs