Solve for d. 9 > d + 2 ≥ -18 Write your answer as a compound inequality with integers. Choices: (A)7 > d ≥ -20 (B)7 > d ≥ -16 (C)11 > d ≥ -16 (D)11 > d ≥ -20

Analyze Inequality: Analyze the compound inequality 9 > d + 2 ≥ -18. Which operation should we use to isolate d? In d + 2, 2 is being added to d. Subtraction should be used to isolate d.Isolate Variable: Subtract 2 from all parts of the inequality to isolate d. 9 > d + 2 ≥ -18 9 - 2 > d + 2 - 2 ≥ -18 - 2 7 > d ≥ -20Subtract 2: Check the solution to ensure it makes sense and matches one of the given choices. If we substitute a value for d that is between 7 and -20, it should satisfy the original inequality. Let's test d = 0: 9 > 0 + 2 ≥ -18 9 > 2 ≥ -18 which is true. Therefore, our solution seems correct.

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Math Problems

Algebra 1

Solve compound inequalities

Full solution

Q. Solve for

d

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9 > d + 2 \geq -18

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Write your answer as a compound inequality with integers.

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Choices:

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(A)

7 > d \geq -20

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(B)

7 > d \geq -16

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(C)

11 > d \geq -16

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(D)

11 > d \geq -20

Analyze Inequality: Analyze the compound inequality 9 > d + 2 \geq -18. Which operation should we use to isolate $d$ ? In $d + 2$ , $2$ is being added to $d$ . Subtraction should be used to isolate $d$ .
Isolate Variable: Subtract $2$ from all parts of the inequality to isolate $d$ . $\newline$ 9 > d + 2 \geq -18 $\newline$ 9 - 2 > d + 2 - 2 \geq -18 - 2 $\newline$ 7 > d \geq -20
Subtract $2$ : Check the solution to ensure it makes sense and matches one of the given choices. $\newline$ If we substitute a value for $d$ that is between $7$ and $-20$ , it should satisfy the original inequality. $\newline$ Let's test $d = 0$ : $\newline$ 9 > 0 + 2 \geq -18 $\newline$ 9 > 2 \geq -18 which is true. $\newline$ Therefore, our solution seems correct.