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Solve for $r$ . $\newline$ $r - 6 \geq 13$ or $r + 13 \leq 8$ $\newline$ Write your answer as a compound inequality with integers. $\newline$ Choices: $\newline$ (A) $r \geq 19$ or $r \leq -5$ $\newline$ (B) $r > 19$ or $r < -5$ $\newline$ (C) $r > 19$ or $r \leq -5$ $\newline$ (D) $r \geq 19$ or $r < -5$

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Solve compound inequalities

Full solution

Q. Solve for

r

.

\newline

r - 6 \geq 13

or

r + 13 \leq 8

\newline

Write your answer as a compound inequality with integers.

\newline

Choices:

\newline

(A)

r \geq 19

or

r \leq -5

\newline

(B)

r > 19

or

r < -5

\newline

(C)

r > 19

or

r \leq -5

\newline

(D)

r \geq 19

or

r < -5

Addition to isolate r: To solve the inequality $r - 6 \geq 13$ , we need to isolate $r$ by adding $6$ to both sides of the inequality. $\newline$ Calculation: $r - 6 + 6 \geq 13 + 6$ $\newline$ Result: $r \geq 19$
Subtraction to isolate $r$ : To solve the inequality $r + 13 \leq 8$ , we need to isolate $r$ by subtracting $13$ from both sides of the inequality. $\newline$ Calculation: $r + 13 - 13 \leq 8 - 13$ $\newline$ Result: $r \leq -5$
Combining compound inequality: Now we combine both parts of the compound inequality to get the final answer. $\newline$ The compound inequality is $r \geq 19$ or $r \leq -5$ .

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