Question
Solve for the variable c in the following equation: $\frac {42}{c-5}=7$
12.6
11
6.7
8.
12.6
11
6.7
8.
Answers
Answered by
GPT-4o mini
To solve the equation
\[
\frac{42}{c-5} = 7,
\]
we start by eliminating the fraction. We do this by multiplying both sides of the equation by \(c - 5\):
\[
42 = 7(c - 5).
\]
Next, we distribute the 7 on the right side:
\[
42 = 7c - 35.
\]
Now, we isolate the term involving \(c\) by adding 35 to both sides:
\[
42 + 35 = 7c.
\]
Simplifying the left side gives us:
\[
77 = 7c.
\]
Next, we solve for \(c\) by dividing both sides by 7:
\[
c = \frac{77}{7} = 11.
\]
Thus, the solution for \(c\) is
\[
\boxed{11}.
\]
\[
\frac{42}{c-5} = 7,
\]
we start by eliminating the fraction. We do this by multiplying both sides of the equation by \(c - 5\):
\[
42 = 7(c - 5).
\]
Next, we distribute the 7 on the right side:
\[
42 = 7c - 35.
\]
Now, we isolate the term involving \(c\) by adding 35 to both sides:
\[
42 + 35 = 7c.
\]
Simplifying the left side gives us:
\[
77 = 7c.
\]
Next, we solve for \(c\) by dividing both sides by 7:
\[
c = \frac{77}{7} = 11.
\]
Thus, the solution for \(c\) is
\[
\boxed{11}.
\]
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