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Solve for $c$ . $\newline$ $-16 < c - 14 < 1$ $\newline$ Write your answer as a compound inequality with integers. $\newline$ Choices: $\newline$ (A) $c < -2$ or $c \geq 15$ $\newline$ (B) $-2 < c < 15$ $\newline$ (C) $-2 < c \leq 15$ $\newline$ (D) $c < -2$ or $c > 15$

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Solve advanced linear inequalities

Full solution

Q. Solve for

c

.

\newline

-16 < c - 14 < 1

\newline

Write your answer as a compound inequality with integers.

\newline

Choices:

\newline

(A)

c < -2

or

c \geq 15

\newline

(B)

-2 < c < 15

\newline

(C)

-2 < c \leq 15

\newline

(D)

c < -2

or

c > 15

Isolate c in compound inequality: First, we will isolate $c$ in the compound inequality by adding $14$ to all three parts of the inequality. $\newline$ $-16 < c - 14 < 1$ $\newline$ $-16 + 14 < c - 14 + 14 < 1 + 14$ $\newline$ $-2 < c < 15$
Determine range for $c$ : Now that we have isolated $c$ , we can see that $c$ must be greater than $-2$ and less than $15$ . This is already in the form of a compound inequality with integers.
Compare with given choices: We compare our result with the given choices to find the correct one. Our result is $-2 < c < 15$ , which matches choice $(B)$ .

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