Analyze Compound Inequality: Analyze the given compound inequality 8 < g + 10 ≤ 16. Which operation should we use to isolate g? In g + 10, 10 is being added to g. Subtraction should be used to isolate g.Use Subtraction to Isolate: Subtract 10 from all parts of the inequality to isolate g. 8 < g + 10 ≤ 16 8 - 10 < g + 10 - 10 ≤ 16 - 10 -2 < g ≤ 6Check Solution: Check the solution to ensure that it makes sense. If g is just greater than -2 and less than or equal to 6, then g + 10 should be just greater than 8 and less than or equal to 16, which is true.

Algebra 1

Solve compound inequalities

Full solution

Q. Solve for

g

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8 < g + 10 \leq 16

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Write your answer as a compound inequality with integers.

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Choices:

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(A)

g < -2

g \geq 6

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(B)

-2 < g \leq 6

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(C)

-2 < g < 6

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(D)

g < -2

g > 6

Analyze Compound Inequality: Analyze the given compound inequality 8 < g + 10 \leq 16. Which operation should we use to isolate $g$ ? In $g + 10$ , $10$ is being added to $g$ . Subtraction should be used to isolate $g$ .
Use Subtraction to Isolate: Subtract $10$ from all parts of the inequality to isolate $g$ . $\newline$ 8 < g + 10 \leq 16 $\newline$ 8 - 10 < g + 10 - 10 \leq 16 - 10 $\newline$ -2 < g \leq 6
Check Solution: Check the solution to ensure that it makes sense. $\newline$ If $g$ is just greater than $-2$ and less than or equal to $6$ , then $g + 10$ should be just greater than $8$ and less than or equal to $16$ , which is true.