Question

solve each inequality. check to justify your work.

1. ( 31+(-2)+e leq \frac{2 e}{3} ) 25. ( 6 s-3-2 s geq 2 s-1.4 ) 26. ( 9 h-3 \frac{1}{5} geq 10 h+\frac{12}{2} )

graph each compound inequality.

1. ( x>-3 ) and ( x leq 1 ) 28. ( x>4 ) or ( x<-2 ) 29. ( 0 leq x leq 5 )

write a compound inequality for each graph.

1. 31. 32.

Explanation:

for 24:

Step1: Simplify left side

$3(-1) + e = -3 + e$

Step2: Multiply by 3 to eliminate fraction

$-9 + 3e \leq 2e$

Step3: Subtract 3e from both sides

$-9 \leq -e$

Step4: Multiply by -1 (reverse inequality)

$9 \geq e$ or $e \leq 9$

for 25:

Step1: Combine like terms on left

$4s - 3 \geq 2s - 1.4$

Step2: Subtract 2s from both sides

$2s - 3 \geq -1.4$

Step3: Add 3 to both sides

$2s \geq 1.6$

Step4: Divide by 2

$s \geq 0.8$

for 26:

Step1: Convert to decimals/mixed numbers

$9h - 3.2 \geq 10h + 6$

Step2: Subtract 9h from both sides

$-3.2 \geq h + 6$

Step3: Subtract 6 from both sides

$-9.2 \geq h$ or $h \leq -\frac{46}{5}$

for 27:

Step1: Identify solution set

All x between -3 (excluded) and 1 (included): $-3 < x \leq 1$

Step2: Graph description

Open circle at -3, closed circle at 1, shade between them.

Answer:

1. $e \leq 9$
2. $s \geq 0.8$
3. $h \leq -\frac{46}{5}$
4. Graph: Open circle at -3, closed circle at 1, shade between
5. Graph: Open circles at 4 (shade right) and -2 (shade left)
6. Graph: Closed circles at 0 and 5, shade between
7. $x = -3$ or $x = 2$
8. $-4 < x < 2$
9. $x < -4$ or $x > 2$