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Solve for $x$ . $\newline$ $-1 > x - 15 \geq -17$ $\newline$ Write your answer as a compound inequality with integers. $\newline$ Choices: $\newline$ (A) $14 \geq x \geq -2$ $\newline$ (B) $14 > x > -2$ $\newline$ (C) $14 > x \geq -2$ $\newline$ (D) $14 \geq x > -2$

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Solve compound inequalities

Full solution

Q. Solve for

x

.

\newline

-1 > x - 15 \geq -17

\newline

Write your answer as a compound inequality with integers.

\newline

Choices:

\newline

(A)

14 \geq x \geq -2

\newline

(B)

14 > x > -2

\newline

(C)

14 > x \geq -2

\newline

(D)

14 \geq x > -2

Undo subtraction of $15$ : To isolate $x$ , we need to undo the subtraction of $15$ from $x$ . We do this by adding $15$ to each part of the inequality. $\newline$ $-1 + 15 > x - 15 + 15 \geq -17 + 15$
Perform addition: Perform the addition for each part of the inequality. $14 > x \geq -2$
Rewrite in interval notation: The inequality $14 > x \geq -2$ can be rewritten in interval notation as $(C)14 > x \geq -2$ , which matches one of the given choices.

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