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Solve for $r$ . $\newline$ $-2 \leq r + 15 < 15$ $\newline$ Write your answer as a compound inequality with integers. $\newline$ Choices: $\newline$ (A) $13 \leq r < 30$ $\newline$ (B) $-17 \leq r < 30$ $\newline$ (C) $-17 \leq r < 0$ $\newline$ (D) $13 \leq r < 0$

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Solve compound inequalities

Full solution

Q. Solve for

r

.

\newline

-2 \leq r + 15 < 15

\newline

Write your answer as a compound inequality with integers.

\newline

Choices:

\newline

(A)

13 \leq r < 30

\newline

(B)

-17 \leq r < 30

\newline

(C)

-17 \leq r < 0

\newline

(D)

13 \leq r < 0

Analyze Compound Inequality: Analyze the given compound inequality $-2 \leq r + 15 < 15$ . Which operation should we use to isolate $r$ ? In $r + 15$ , $15$ is being added to $r$ . Subtraction should be used to isolate $r$ .
Isolate Variable Using Subtraction: Solve for $r$ by subtracting $15$ from all parts of the inequality. $\newline$ $-2 \leq r + 15 < 15$ $\newline$ $-2 - 15 \leq r + 15 - 15 < 15 - 15$ $\newline$ $-17 \leq r < 0$

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