Question

name:score:solving & graphing inequalitiessolve each inequality and graph the solution.1) $\frac{x}{2}+3>9$2) $4x + 5 \leq 13$3) $7x - 19 < 16$4) $\frac{x - 4}{5} \geq 2$5) $9 + 3x > 12$6) $3x - 4 \leq 5$7) $\frac{x}{8}+1 < 3$8) $2x + 5 \geq 19$

Explanation:

1) Step1: Subtract 3 from both sides

$\frac{x}{2} + 3 - 3 > 9 - 3$
$\frac{x}{2} > 6$

1) Step2: Multiply by 2 on both sides

$\frac{x}{2} \times 2 > 6 \times 2$
$x > 12$

2) Step1: Subtract 5 from both sides

$4x + 5 - 5 \leq 13 - 5$
$4x \leq 8$

2) Step2: Divide by 4 on both sides

$\frac{4x}{4} \leq \frac{8}{4}$
$x \leq 2$

3) Step1: Add 19 to both sides

$7x - 19 + 19 < 16 + 19$
$7x < 35$

3) Step2: Divide by 7 on both sides

$\frac{7x}{7} < \frac{35}{7}$
$x < 5$

4) Step1: Multiply by 5 on both sides

$\frac{x-4}{5} \times 5 \geq 2 \times 5$
$x - 4 \geq 10$

4) Step2: Add 4 to both sides

$x - 4 + 4 \geq 10 + 4$
$x \geq 14$

5) Step1: Subtract 9 from both sides

$9 + 3x - 9 > 12 - 9$
$3x > 3$

5) Step2: Divide by 3 on both sides

$\frac{3x}{3} > \frac{3}{3}$
$x > 1$

6) Step1: Add 4 to both sides

$3x - 4 + 4 \leq 5 + 4$
$3x \leq 9$

6) Step2: Divide by 3 on both sides

$\frac{3x}{3} \leq \frac{9}{3}$
$x \leq 3$

7) Step1: Subtract 1 from both sides

$\frac{x}{8} + 1 - 1 < 3 - 1$
$\frac{x}{8} < 2$

7) Step2: Multiply by 8 on both sides

$\frac{x}{8} \times 8 < 2 \times 8$
$x < 16$

8) Step1: Subtract 5 from both sides

$2x + 5 - 5 \geq 19 - 5$
$2x \geq 14$

8) Step2: Divide by 2 on both sides

$\frac{2x}{2} \geq \frac{14}{2}$
$x \geq 7$

Answer:

1. $x > 12$ (Graph: Open circle at 12, arrow pointing right)
2. $x \leq 2$ (Graph: Closed circle at 2, arrow pointing left)
3. $x < 5$ (Graph: Open circle at 5, arrow pointing left)
4. $x \geq 14$ (Graph: Closed circle at 14, arrow pointing right)
5. $x > 1$ (Graph: Open circle at 1, arrow pointing right)
6. $x \leq 3$ (Graph: Closed circle at 3, arrow pointing left)
7. $x < 16$ (Graph: Open circle at 16, arrow pointing left)
8. $x \geq 7$ (Graph: Closed circle at 7, arrow pointing right)