Question

solve the inequality. then graph the solution.

1. $\frac{c}{3} > -13$

$\frac{c}{3} \cdot 3 > -13 \cdot 3$
$c > -39$
(number line graph from -50 to 0 with open circle at -40 and arrow right)

1. $\frac{x}{1.9} > -0.01$
2. $\frac{q}{0.7} \geq -9.3$
3. $\frac{k}{7} \leq -7 + 21$
4. $12 > 1\frac{1}{6}b - b$
5. $8 - (-8) \geq -r + \frac{2}{3}r$
6. $\frac{s}{10} \geq -3(10 + 1)$
7. $-\frac{i}{3} + \frac{2i}{3} < -30 - 4$
8. $-1\frac{1}{2}c + c > -9 + 19$

Explanation:

Step1: Solve for x

Multiply both sides by 1.9: $x > -0.01 \times 1.9$
$x > -0.019$

Step2: Solve for k

Simplify right side: $\frac{k}{7} \leq 14$
Multiply by 7: $k \leq 98$

Step3: Solve for b

Simplify right side: $12 > \frac{1}{6}b$
Multiply by 6: $b < 72$

Step4: Solve for r

Simplify both sides: $16 \geq -\frac{1}{3}r$
Multiply by -3 (reverse inequality): $r \geq -48$

Step5: Solve for s

Simplify right side: $\frac{s}{10} \geq -33$
Multiply by 10: $s \geq -330$

Step6: Solve for i

Simplify left side: $\frac{i}{3} < -34$
Multiply by 3: $i < -102$

Step7: Solve for c

Simplify left side: $-\frac{1}{2}c > 10$
Multiply by -2 (reverse inequality): $c < -20$

Answer:

1. $x > -0.019$
2. $k \leq 98$
3. $b < 72$
4. $r \geq -48$
5. $s \geq -330$
6. $i < -102$
7. $c < -20$

(Graphs for each solution: Open circle at boundary for >/<, closed circle for ≥/≤; shade right for >/≥, left for </≤.)