Solve for m. m + 8 ≤ 14 or m - 5 > 15 Write your answer as a compound inequality with integers. Choices: (A)m ≤ 6 or m > 20 (B)m ≤ 22 or m > 10 (C)m ≤ 22 or m > 20 (D)m ≤ 6 or m > 10

Isolate m in first inequality: We have two separate inequalities to solve: m + 8 ≤ 14 and m - 5 > 15. Let's start with the first inequality m + 8 ≤ 14. To isolate m, we need to subtract 8 from both sides of the inequality. m + 8 - 8 ≤ 14 - 8 m ≤ 6Isolate m in second inequality: Now let's solve the second inequality m - 5 > 15. To isolate m, we need to add 5 to both sides of the inequality. m - 5 + 5 > 15 + 5 m > 20Combine solutions: Combining the solutions from both inequalities, we get the compound inequality: m ≤ 6 or m > 20 This matches one of the given choices.

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Math Problems

Algebra 1

Solve compound inequalities

Full solution

Q. Solve for

m

\newline

m + 8 \leq 14

m - 5 > 15

\newline

Write your answer as a compound inequality with integers.

\newline

Choices:

\newline

(A)

m \leq 6

m > 20

\newline

(B)

m \leq 22

m > 10

\newline

(C)

m \leq 22

m > 20

\newline

(D)

m \leq 6

m > 10

Isolate $m$ in first inequality: We have two separate inequalities to solve: $m + 8 \leq 14$ and m - 5 > 15. Let's start with the first inequality $m + 8 \leq 14$ . $\newline$ To isolate $m$ , we need to subtract $8$ from both sides of the inequality. $\newline$ $m + 8 - 8 \leq 14 - 8$ $\newline$ $m \leq 6$
Isolate $m$ in second inequality: Now let's solve the second inequality m - 5 > 15. To isolate $m$ , we need to add $5$ to both sides of the inequality. m - 5 + 5 > 15 + 5 m > 20
Combine solutions: Combining the solutions from both inequalities, we get the compound inequality: $\newline$ $m \leq 6$ or m > 20 $\newline$ This matches one of the given choices.