Solve for r. r - 6 ≥ 13 or r + 13 ≤ 8 Write your answer as a compound inequality with integers. Choices: (A)r ≥ 19 or r ≤ -5 (B)r > 19 or r 19 or r ≤ -5 (D)r ≥ 19 or r < -5

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

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Math Problems

Algebra 1

Solve compound inequalities

Full solution

Q. Solve for

r

\newline

r - 6 \geq 13

r + 13 \leq 8

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Write your answer as a compound inequality with integers.

\newline

Choices:

\newline

(A)

r \geq 19

r \leq -5

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(B)

r > 19

r < -5

\newline

(C)

r > 19

r \leq -5

\newline

(D)

r \geq 19

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 $r \leq -5$ .