Solved on Dec 01, 2023

Find the value of cc that satisfies the equation 7=c+1237 = \frac{c+12}{3}, which has solutions c=9c = -9 and c=9c = 9.

STEP 1

Assumptions
1. The equation is given as 7=c+1237=\frac{c+12}{3}.
2. The possible values of cc are 9-9 and 99.

STEP 2

First, we need to substitute the possible values of cc into the equation and check if the equation holds true. Let's start with c=9c=-9.
7=9+1237=\frac{-9+12}{3}

STEP 3

Perform the addition in the numerator of the fraction.
7=337=\frac{3}{3}

STEP 4

Perform the division.
7=17=1

STEP 5

We see that when c=9c=-9, the equation does not hold true, as 717 \neq 1. Now, let's substitute c=9c=9 into the equation.
7=9+1237=\frac{9+12}{3}

STEP 6

Perform the addition in the numerator of the fraction.
7=2137=\frac{21}{3}

STEP 7

Perform the division.
7=77=7

STEP 8

We see that when c=9c=9, the equation holds true, as 7=77 = 7.
So, the value of cc that is a solution to this equation is c=9c=9.

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