Solve for q. q + 18 ≤ 4 or q - 5 > 10 Write your answer as a compound inequality with integers. Choices: (A)q ≤ 22 or q > 15 (B)q ≤ 22 or q > 5 (C)q ≤ -14 or q > 5 (D)q ≤ -14 or q > 15

Isolate q in first part: Solve the first part of the compound inequality. We have q + 18 ≤ 4. To isolate q, we need to subtract 18 from both sides of the inequality. q + 18 - 18 ≤ 4 - 18 q ≤ -14Isolate q in second part: Solve the second part of the compound inequality. We have q - 5 > 10. To isolate q, we need to add 5 to both sides of the inequality. q - 5 + 5 > 10 + 5 q > 15Combine solutions for final inequality: Combine the solutions from Step 1 and Step 2 to write the final compound inequality. The solution is q ≤ -14 or q > 15.

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Math Problems

Algebra 1

Solve compound inequalities

Full solution

Q. Solve for

q

\newline

q + 18 \leq 4

q - 5 > 10

\newline

Write your answer as a compound inequality with integers.

\newline

Choices:

\newline

(A)

q \leq 22

q > 15

\newline

(B)

q \leq 22

q > 5

\newline

(C)

q \leq -14

q > 5

\newline

(D)

q \leq -14

q > 15

Isolate $q$ in first part: Solve the first part of the compound inequality. $\newline$ We have $q + 18 \leq 4$ . To isolate $q$ , we need to subtract $18$ from both sides of the inequality. $\newline$ $q + 18 - 18 \leq 4 - 18$ $\newline$ $q \leq -14$
Isolate q in second part: Solve the second part of the compound inequality. $\newline$ We have q - 5 > 10. To isolate q, we need to add $5$ to both sides of the inequality. $\newline$ q - 5 + 5 > 10 + 5 $\newline$ q > 15
Combine solutions for final inequality: Combine the solutions from Step $1$ and Step $2$ to write the final compound inequality. $\newline$ The solution is $q \leq -14$ or q > 15.