Question

Solve for C -3 (C + 5)- (c-3)=32

Answer 1

Given the equation:

`-3(c+5)-(c-3)=32`

To find the value of 'c', the first step to do is to get rid of the parenthesis. We can do this using the distributive property on both cases:

`\begin{gathered} -3(c+5)-(c-3)=32 \\ \Rightarrow-3\cdot c+(-3)\cdot5-c-(-3)=32 \\ \Rightarrow-3c-15-c+3=32 \end{gathered}`

Now that we don't have any parenthesis in our equation, we start moving similar terms: we leave on the left the terms with the variable 'c' and we move the rest of the terms to the right side with it's sign changed:

`\begin{gathered} -3c-15-c+3=32 \\ \Rightarrow-3c-c=32+15-3 \end{gathered}`

We can make the operations on each side since now we have the similar terms apart:

`\begin{gathered} -3c-c=32+15-3 \\ \Rightarrow-4c=47-3=44 \\ -4c=44 \end{gathered}`

Finally, we move the -4 that is multiplying the 'c' to the other side doing its opposite operation:

`\begin{gathered} -4c=44 \\ \Rightarrow c=(44)/(-4)=-11 \\ c=-11 \end{gathered}`

therefore, c=-11