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

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Solve compound inequalities

Full solution

Q. Solve for

m

.

\newline

m + 8 \leq 14

or

m - 5 > 15

\newline

Write your answer as a compound inequality with integers.

\newline

Choices:

\newline

(A)

m \leq 6

or

m > 20

\newline

(B)

m \leq 22

or

m > 10

\newline

(C)

m \leq 22

or

m > 20

\newline

(D)

m \leq 6

or

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.

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