Analyze Compound Inequality: Analyze the given compound inequality. The inequality 6 < z - 5 < 9 involves a single variable z. To solve for z, we need to isolate it by performing the same operation on all three parts of the inequality.Add 5 to All Parts: Add 5 to all three parts of the inequality. To isolate z, we add 5 to each part of the compound inequality because z - 5 has 5 being subtracted from z. 6 < z - 5 < 9 6 + 5 < z - 5 + 5 < 9 + 5 11 < z < 14Write Solution as Compound Inequality: Write the solution as a compound inequality with integers. The solution to the inequality is 11 < z < 14, which matches one of the given choices.

Algebra 1

Solve compound inequalities

Full solution

Q. Solve for

z

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6 < z - 5 < 9

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Write your answer as a compound inequality with integers.

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Choices:

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(A)

11 < z < 14

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(B)

11 < z \leq 14

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(C)

z < 11

z \geq 14

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(D)

z < 11

z > 14

Analyze Compound Inequality: Analyze the given compound inequality. $\newline$ The inequality 6 < z - 5 < 9 involves a single variable $z$ . To solve for $z$ , we need to isolate it by performing the same operation on all three parts of the inequality.
Add $5$ to All Parts: Add $5$ to all three parts of the inequality. $\newline$ To isolate $z$ , we add $5$ to each part of the compound inequality because $z - 5$ has $5$ being subtracted from $z$ . $\newline$ 6 < z - 5 < 9 $\newline$ 6 + 5 < z - 5 + 5 < 9 + 5 $\newline$ 11 < z < 14
Write Solution as Compound Inequality: Write the solution as a compound inequality with integers. $\newline$ The solution to the inequality is 11 < z < 14, which matches one of the given choices.