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Chapter 3: Problem 6

Can we solve \(3(c+2)+5(2 c-5)=-6 ?\) Why or why not?

Short Answer

Expert verified
Yes, we can solve the given equation \(3(c+2)+5(2c-5)=-6\). By distributing the numbers, combining like terms, and isolating the variable "c," we find a unique solution \(c=1\).

Step by step solution

01

1. Distribute the numbers in the parentheses

First, we will distribute the numbers outside the parentheses to the terms inside, following the distributive property: \(3(c+2)+5(2c-5) \rightarrow 3c+6+10c-25\).
02

2. Combine like terms

Now, combine the "c" terms and constant terms on the left-hand side of the equation: \(3c+6+10c-25 \rightarrow 13c-19\). So, the equation becomes: \(13c-19 = -6\).
03

3. Add 19 to both sides of the equation

To isolate the "c" term, we will add 19 to both sides of the equation: \(13c-19+19 = -6+19\). This simplifies to: \(13c = 13\).
04

4. Divide by 13 to find the value of c

Finally, divide both sides of the equation by 13 to find the value of "c": \(\frac{13c}{13} = \frac{13}{13}\). This gives us: \(c = 1\). Since we have found a unique value for "c" that makes the equation true, we can conclude that the equation has a solution: \(c=1\).

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