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

Analyze Inequality: Analyze the compound inequality 0 > r + 5 ≥ -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 ≥ -8 0 - 5 > r + 5 - 5 ≥ -8 - 5 -5 > r ≥ -13Check Solution: Check the solution to ensure it makes sense. If r is -6, then -5 > -6 is true and -6 ≥ -13 is also true. If r is -12, then -5 > -12 is true and -12 ≥ -13 is also true. The solution -5 > r ≥ -13 is correct.

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Math Problems

Algebra 1

Solve compound inequalities

Full solution

Q. Solve for

r

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0 > r + 5 \geq -8

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Write your answer as a compound inequality with integers.

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Choices:

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(A)

r > -5

r \leq -13

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(B)

-5 > r \geq -13

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(C)

-5 > r > -13

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(D)

r > -5

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 -80 - 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.