How do you solve c + 70 + 12c = 196 - 5c
To solve the equation c + 70 + 12c = 196 - 5c, we need to simplify and combine like terms on both sides of the equation, and then isolate the variable c on one side.
Let's go step by step:
1. Begin by combining like terms on both sides of the equation.
On the left-hand side of the equation, we have c + 70 + 12c. To combine like terms, we add the c terms together and obtain 13c. So, the left-hand side simplifies to 13c + 70.
On the right-hand side of the equation, we have 196 - 5c, which does not require any further simplification.
So, the original equation now becomes: 13c + 70 = 196 - 5c.
2. To isolate the variable c, we need to get all the terms with c on one side of the equation and the constant terms on the other side.
To do this, we can add 5c to both sides of the equation.
(13c + 70) + 5c = (196 - 5c) + 5c
13c + 5c + 70 = 196 - 0c (the -5c and +5c cancel each other out)
18c + 70 = 196
3. Now, we can isolate the term with c by subtracting 70 from both sides of the equation.
(18c + 70) - 70 = 196 - 70
18c = 126
4. Finally, to solve for c, we divide both sides of the equation by 18.
18c/18 = 126/18
c = 7
Thus, the solution to the equation c + 70 + 12c = 196 - 5c is c = 7.