Solve for r. r + 20 ≤ 4 or r + 8 > 6 Write your answer as a compound inequality with integers. Choices: (A)r ≤ -16 or r > -2 (B)r ≤ 24 or r > 14 (C)r ≤ 24 or r > -2 (D)r ≤ -16 or r > 14

Isolate r in first inequality: To solve the inequality r + 20 ≤ 4, we need to isolate r. We do this by subtracting 20 from both sides of the inequality. r + 20 - 20 ≤ 4 - 20 r ≤ -16Isolate r in second inequality: Now, we solve the second part of the compound inequality r + 8 > 6. Again, we isolate r by subtracting 8 from both sides. r + 8 - 8 > 6 - 8 r > -2Combine results for compound inequality: We have now solved both parts of the compound inequality. The solution is a compound inequality that combines both results. r ≤ -16 or r > -2

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Math Problems

Algebra 1

Solve compound inequalities

Full solution

Q. Solve for

r

\newline

r + 20 \leq 4

r + 8 > 6

\newline

Write your answer as a compound inequality with integers.

\newline

Choices:

\newline

(A)

r \leq -16

r > -2

\newline

(B)

r \leq 24

r > 14

\newline

(C)

r \leq 24

r > -2

\newline

(D)

r \leq -16

r > 14

Isolate $r$ in first inequality: To solve the inequality $r + 20 \leq 4$ , we need to isolate $r$ . We do this by subtracting $20$ from both sides of the inequality. $\newline$ $r + 20 - 20 \leq 4 - 20$ $\newline$ $r \leq -16$
Isolate $r$ in second inequality: Now, we solve the second part of the compound inequality r + 8 > 6. Again, we isolate $r$ by subtracting $8$ from both sides. $\newline$ r + 8 - 8 > 6 - 8 $\newline$ r > -2
Combine results for compound inequality: We have now solved both parts of the compound inequality. The solution is a compound inequality that combines both results. $r \leq -16$ or r > -2