Question

practice & problem solving
leveled practice in 6-9, fill in the boxes to solve the inequality. then graph
the solution.
6.
$8m \leq 56$
$8m \leq 56$
$m \leq \square$
7.
$\boldsymbol{-\frac{4}{3}x < -8}$
$\square \cdot -\frac{4}{3}x < -8 \cdot \square$
$x \circ \square$
8.
$-7x > 56$
$\frac{-7x}{\square} \circ \frac{56}{\square}$
$x \circ \square$
9.
$\boldsymbol{\frac{m}{-5} \geq 2}$
$\square \cdot \frac{m}{-5} \circ 2 \cdot \square$
$m \circ \square$

1. kyra and five friends shared a bag of fruit

snacks. each person got no more than 3 fruit
snacks. the inequality $x \div 6 \leq 3$ represents
this situation. solve the inequality to find the
possible numbers of fruit snacks that were in
the bag.

1. over the next 17 months, eli needs to read more

than 102 e-books. the inequality $17x > 102$
represents the number of e-books he needs to
read per month. solve the inequality to find the
number of e-books eli needs to read per month.

1. brittney can spend no more than $15 for new fish in her aquarium.

a. let $f$ be the number of fish she can buy.
what inequality represents the problem?
b. how many fish can brittney buy?
$3.00 each$
5-5 solve inequalities using multiplication or division 293

Explanation:

Step1: Solve $8m \leq 56$

Divide both sides by 8:
$\frac{8m}{8} \leq \frac{56}{8}$
$m \leq 7$
(Graph: Closed dot at 7, shade left)

Step2: Solve $-\frac{4}{3}x < -8$

Multiply by $-\frac{3}{4}$, reverse inequality:
$-\frac{3}{4} \cdot -\frac{4}{3}x > -8 \cdot -\frac{3}{4}$
$x > 6$
(Graph: Open dot at 6, shade right)

Step3: Solve $-7x > 56$

Divide by -7, reverse inequality:
$\frac{-7x}{-7} < \frac{56}{-7}$
$x < -8$
(Graph: Open dot at -8, shade left)

Step4: Solve $\frac{m}{3} \geq 2$

Multiply both sides by 3:
$3 \cdot \frac{m}{3} \geq 2 \cdot 3$
$m \geq 6$
(Graph: Closed dot at 6, shade right)

Step5: Solve $x \div 6 \leq 3$

Multiply by 6:
$x \leq 3 \cdot 6$
$x \leq 18$

Step6: Solve $17x > 102$

Divide by 17:
$\frac{17x}{17} > \frac{102}{17}$
$x > 6$

Step7: Write inequality for Q12a

Cost per fish is $3, total ≤ $15:
$3f \leq 15$

Step8: Solve Q12b inequality

Divide by 3:
$\frac{3f}{3} \leq \frac{15}{3}$
$f \leq 5$

Answer:

1. $m \leq 7$ (Graph: Closed dot at 7, shade left)
2. $x > 6$ (Graph: Open dot at 6, shade right)
3. $x < -8$ (Graph: Open dot at -8, shade left)
4. $m \geq 6$ (Graph: Closed dot at 6, shade right)
5. At most 18 fruit snacks
6. More than 6 e-books per month

12a. $3f \leq 15$
12b. At most 5 fish