Solve for q. q + 20 ≤ 14 or q + 16 ≥ 20 Write your answer as a compound inequality with integers. Choices: (A)q ≤ -6 or q ≥ 4 (B)q ≤ 34 or q ≥ 36 (C)q ≤ 34 or q ≥ 4 (D)q ≤ -6 or q ≥ 36

First Inequality Solution: We have two separate inequalities to solve: q + 20 ≤ 14 and q + 16 ≥ 20. Let's start with the first inequality, q + 20 ≤ 14. To isolate q, we need to subtract 20 from both sides of the inequality. q + 20 - 20 ≤ 14 - 20 q ≤ -6Second Inequality Solution: Now let's solve the second inequality, q + 16 ≥ 20. To isolate q, we subtract 16 from both sides of the inequality. q + 16 - 16 ≥ 20 - 16 q ≥ 4Compound Inequality Solution: We have now solved both inequalities. The solution to the compound inequality is: q ≤ -6 or q ≥ 4

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Math Problems

Algebra 1

Solve compound inequalities

Full solution

Q. Solve for

q

\newline

q + 20 \leq 14

q + 16 \geq 20

\newline

Write your answer as a compound inequality with integers.

\newline

Choices:

\newline

(A)

q \leq -6

q \geq 4

\newline

(B)

q \leq 34

q \geq 36

\newline

(C)

q \leq 34

q \geq 4

\newline

(D)

q \leq -6

q \geq 36

First Inequality Solution: We have two separate inequalities to solve: $q + 20 \leq 14$ and $q + 16 \geq 20$ . Let's start with the first inequality, $q + 20 \leq 14$ . $\newline$ To isolate $q$ , we need to subtract $20$ from both sides of the inequality. $\newline$ $q + 20 - 20 \leq 14 - 20$ $\newline$ $q \leq -6$
Second Inequality Solution: Now let's solve the second inequality, $q + 16 \geq 20$ . To isolate $q$ , we subtract $16$ from both sides of the inequality. $q + 16 - 16 \geq 20 - 16$ $q \geq 4$
Compound Inequality Solution: We have now solved both inequalities. The solution to the compound inequality is: $q \leq -6$ or $q \geq 4$