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Solve for $r$ . $\newline$ $0 > r + 5 \geq -8$ $\newline$ Write your answer as a compound inequality with integers. $\newline$ Choices: $\newline$ (A) $r > -5$ or $r \leq -13$ $\newline$ (B) $-5 > r \geq -13$ $\newline$ (C) $-5 > r > -13$ $\newline$ (D) $r > -5$ or $r < -13$

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Solve compound inequalities

Full solution

Q. Solve for

r

.

\newline

0 > r + 5 \geq -8

\newline

Write your answer as a compound inequality with integers.

\newline

Choices:

\newline

(A)

r > -5

or

r \leq -13

\newline

(B)

-5 > r \geq -13

\newline

(C)

-5 > r > -13

\newline

(D)

r > -5

or

r < -13

Analyze Inequality: Analyze the compound inequality $0 > r + 5 \geq -8$ . Which operation should we use to isolate $r$ ? In $r + 5$ , $5$ is being added to $r$ . Subtraction should be used to isolate $r$ .
Isolate r Using Subtraction: Solve for r by subtracting $5$ from all parts of the inequality. $0 > r + 5 \geq -8$ $0 - 5 > r + 5 - 5 \geq -8 - 5$ $-5 > r \geq -13$
Check Solution: Check the solution to ensure it makes sense. $\newline$ If $r$ is $-6$ , then $-5 > -6$ is true and $-6 \geq -13$ is also true. $\newline$ If $r$ is $-12$ , then $-5 > -12$ is true and $-12 \geq -13$ is also true. $\newline$ The solution $-5 > r \geq -13$ is correct.

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