Question

-13 ≤ 3 + 8p ≤ 11
??????

Answer 1

Answer:
`-2 \le p \le 1`

Work Shown

`-13 \le 3 + 8p \le 11\\\\-13-3 \le 3 + 8p-3 \le 11-3 \ \text{ see note1}\\\\-16 \le 8p \le 8\\\\-16/8 \le 8p/8 \le 8/8 \ \text{ see note2}\\\\-2 \le p \le 1\\\\`

• note1: Subtract 3 from all sides.
• note2: Divide all sides by 8. The inequality signs do not flip (they only do so if we divided all sides by a negative number).

The graph of this will have closed filled in circles at -2 and 1 on the number line. Shade in between those endpoints. If p was an integer, then the integer solutions would be {-2, -1, 0, 1}