Question

1. $168 \geq 8(5 + 2x)$
2. $250 \leq 5(1 - 7x)$

solve each compound inequality and graph its solution.

1. $-2x \leq -18$ or $9x < 36$
2. $-13 \leq x - 8 < -9$
3. $-8 \leq n + 2 \leq -3$
4. $x + 2 \leq -8$ or $x - 2 > 7$

Explanation:

Problem 5: \( 168 \geq 8(5 + 2x) \)

Step 1: Distribute the 8

\( 168 \geq 40 + 16x \)

Step 2: Subtract 40 from both sides

\( 128 \geq 16x \)

Step 3: Divide both sides by 16

\( 8 \geq x \) or \( x \leq 8 \)

Step 1: Distribute the 5

\( 250 \leq 5 - 35x \)

Step 2: Subtract 5 from both sides

\( 245 \leq -35x \)

Step 3: Divide both sides by -35 (and reverse inequality)

\( -7 \geq x \) or \( x \leq -7 \)

For \( -2x \leq -18 \):

Step 1: Divide by -2 (reverse inequality)

\( x \geq 9 \)

For \( 9x < 36 \):

Step 1: Divide by 9

\( x < 4 \)

Answer:

\( x \leq 8 \)

Problem 16: \( 250 \leq 5(1 - 7x) \)