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Solve for $d$ . $\newline$ $-3 > d - 20 > -7$ $\newline$ Write your answer as a compound inequality with integers. $\newline$ Choices: $\newline$ (A) $17 \geq d > 13$ $\newline$ (B) $d > 17$ or $d < 13$ $\newline$ (C) $17 > d > 13$ $\newline$ (D) $d \geq 17$ or $d < 13$

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Solve compound inequalities

Full solution

Q. Solve for

d

.

\newline

-3 > d - 20 > -7

\newline

Write your answer as a compound inequality with integers.

\newline

Choices:

\newline

(A)

17 \geq d > 13

\newline

(B)

d > 17

or

d < 13

\newline

(C)

17 > d > 13

\newline

(D)

d \geq 17

or

d < 13

Analyze Compound Inequality: Analyze the compound inequality $-3 > d - 20 > -7$ . $\newline$ Which operation should we use to isolate $d$ ? $\newline$ In $d - 20$ , $20$ is being subtracted from $d$ . $\newline$ Addition should be used to isolate $d$ .
Use Addition to Isolate: Add $20$ to all parts of the inequality $-3 > d - 20 > -7$ . $\newline$ $-3 + 20 > d - 20 + 20 > -7 + 20$ $\newline$ $17 > d > 13$ $\newline$ This gives us the compound inequality with $d$ isolated.
Add $20$ to All Parts: Check the inequality signs to ensure they are correct. $\newline$ The original inequality was $-3 > d - 20 > -7$ . After adding $20$ to all parts, the inequality signs should still point in the same direction, and the resulting inequality should be $17 > d > 13$ .

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