Solve for m. -7 ≤ m - 20 ≤ -2 Write your answer as a compound inequality with integers. Choices: (A)13 ≤ m ≤ 18 (B)13 ≤ m ≤ -22 (C)-27 ≤ m ≤ 18 (D)-27 ≤ m ≤ -22

Analyze Compound Inequality: Analyze the given compound inequality -7 ≤ m - 20 ≤ -2. Which operation should we use to isolate m? In m - 20, 20 is being subtracted from m. Addition should be used to isolate m.Use Addition to Isolate: Add 20 to all three parts of the inequality to isolate m. -7 ≤ m - 20 ≤ -2 -7 + 20 ≤ m - 20 + 20 ≤ -2 + 20 13 ≤ m ≤ 18Add 20 to Isolate: Check the solution to ensure it makes sense. Plug in the endpoints to the original inequality to verify. For m = 13: -7 ≤ 13 - 20 ≤ -2 which simplifies to -7 ≤ -7 ≤ -2. This is true. For m = 18: -7 ≤ 18 - 20 ≤ -2 which simplifies to -7 ≤ -2 ≤ -2. This is also true. The solution 13 ≤ m ≤ 18 satisfies the original inequality.

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Solve for $m$ . $\newline$ $-7 \leq m - 20 \leq -2$ $\newline$ Write your answer as a compound inequality with integers. $\newline$ Choices: $\newline$ (A) $13 \leq m \leq 18$ $\newline$ (B) $13 \leq m \leq -22$ $\newline$ (C) $-27 \leq m \leq 18$ $\newline$ (D) $-27 \leq m \leq -22$

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Math Problems

Algebra 1

Solve compound inequalities

Full solution

Q. Solve for

m

\newline

-7 \leq m - 20 \leq -2

\newline

Write your answer as a compound inequality with integers.

\newline

Choices:

\newline

(A)

13 \leq m \leq 18

\newline

(B)

13 \leq m \leq -22

\newline

(C)

-27 \leq m \leq 18

\newline

(D)

-27 \leq m \leq -22

Analyze Compound Inequality: Analyze the given compound inequality $-7 \leq m - 20 \leq -2$ . Which operation should we use to isolate $m$ ? In $m - 20$ , $20$ is being subtracted from $m$ . Addition should be used to isolate $m$ .
Use Addition to Isolate: Add $20$ to all three parts of the inequality to isolate $m$ . $\newline$ $-7 \leq m - 20 \leq -2$ $\newline$ $-7 + 20 \leq m - 20 + 20 \leq -2 + 20$ $\newline$ $13 \leq m \leq 18$
Add $20$ to Isolate: Check the solution to ensure it makes sense. $\newline$ Plug in the endpoints to the original inequality to verify. $\newline$ For $m = 13$ : $-7 \leq 13 - 20 \leq -2$ which simplifies to $-7 \leq -7 \leq -2$ . This is true. $\newline$ For $m = 18$ : $-7 \leq 18 - 20 \leq -2$ which simplifies to $-7 \leq -2 \leq -2$ . This is also true. $\newline$ The solution $13 \leq m \leq 18$ satisfies the original inequality.