Solve for p. p - 5 ≤ 1 or p + 6 ≥ 15 Write your answer as a compound inequality with integers. Choices: (A)p ≤ 6 or p ≥ 21 (B)p ≤ -4 or p ≥ 9 (C)p ≤ -4 or p ≥ 21 (D)p ≤ 6 or p ≥ 9

Solve First Part: Solve the first part of the compound inequality. We have p - 5 ≤ 1. To isolate p, we need to add 5 to both sides of the inequality. p - 5 + 5 ≤ 1 + 5 p ≤ 6Solve Second Part: Solve the second part of the compound inequality. We have p + 6 ≥ 15. To isolate p, we need to subtract 6 from both sides of the inequality. p + 6 - 6 ≥ 15 - 6 p ≥ 9Combine Solutions: Combine the solutions from Step 1 and Step 2 to form the compound inequality. The solution is p ≤ 6 or p ≥ 9.

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Math Problems

Algebra 1

Solve compound inequalities

Full solution

Q. Solve for

p

\newline

p - 5 \leq 1

p + 6 \geq 15

\newline

Write your answer as a compound inequality with integers.

\newline

Choices:

\newline

(A)

p \leq 6

p \geq 21

\newline

(B)

p \leq -4

p \geq 9

\newline

(C)

p \leq -4

p \geq 21

\newline

(D)

p \leq 6

p \geq 9

Solve First Part: Solve the first part of the compound inequality. $\newline$ We have $p - 5 \leq 1$ . To isolate $p$ , we need to add $5$ to both sides of the inequality. $\newline$ $p - 5 + 5 \leq 1 + 5$ $\newline$ $p \leq 6$
Solve Second Part: Solve the second part of the compound inequality. $\newline$ We have $p + 6 \geq 15$ . To isolate $p$ , we need to subtract $6$ from both sides of the inequality. $\newline$ $p + 6 - 6 \geq 15 - 6$ $\newline$ $p \geq 9$
Combine Solutions: Combine the solutions from Step $1$ and Step $2$ to form the compound inequality. $\newline$ The solution is $p \leq 6$ or $p \geq 9$ .