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$Solve for c. Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions. -32 c+12 <= -66 c-16$

Solve for $c$ . Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions. $\newline$ $-32c + 12 \leq -66c - 16$

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Solve multi-step inequalities

Full solution

Q. Solve for

c

. Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions.

\newline

-32c + 12 \leq -66c - 16

Add $66c$ to both sides: We need to isolate the variable $c$ on one side of the inequality. Let's start by adding $66c$ to both sides to move all the $c$ terms to one side. $\newline$ $-32c + 12 + 66c \leq -66c - 16 + 66c$
Combine like terms: Now, let's combine like terms on both sides of the inequality. $\newline$ $(-32c + 66c) + 12 \leq -16$ $\newline$ $34c + 12 \leq -16$
Subtract $12$ from both sides: Next, we subtract $12$ from both sides to isolate the term with c. $\newline$ $34c + 12 - 12 \leq -16 - 12$ $\newline$ $34c \leq -28$
Divide by $34$ : To solve for $c$ , we divide both sides by $34$ , the coefficient of $c$ . $\frac{34c}{34} \leq \frac{-28}{34}$ $c \leq \frac{-28}{34}$
Reduce fraction: Now, we reduce the fraction $-28 / 34$ to its lowest terms. $\newline$ Both $-28$ and $34$ have a common factor of $2$ . $\newline$ $-28 / 34 = (-14) / 17$ $\newline$ c $\leq -14 / 17$

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