Question

How do you find the sum of $(c - 4) + (3c + 9)?$

Answer 1

Hint: To find sum of given algebraic expressions, firstly simplify the expression under parentheses (if any) then open the parentheses and with the help of commutative property of addition, group like terms together (similar variables together and constants together). Then add or subtract (as given) coefficients of the variables and add or subtract constants directly. You will get the required sum.

Complete step by step solution:
In order to find the sum of $(c - 4) + (3c + 9)$, we will first open the parentheses as follows
$
   = (c - 4) + (3c + 9) \\
   = c - 4 + 3c + 9 \\
 $
Now, we will group like terms together, we can see that in the above expression there is only one variable is present (i.e. $c$) so we will group terms with $c$ together and rest terms (constants) together as follows
$ = (c + 3c) + ( - 4 + 9)$
Now, we will perform the addition or subtraction of constants and coefficients of variable, according to their signs
$
   = (1 + 3)c + (9 - 4) \\
   = 4c + 5 \\
 $
Therefore $4c + 5$ is the required sum.

Additional information:
The method we have used to calculate the sum is known as horizontal method. There is one more method called column method in which we write each expression in a separate row in such a way that terms lie on the same column and then add terms column wise.

Note: When opening the parentheses, check for the sign before the parentheses if it is positive or negative, if it is positive then open the parentheses normally, but if negative then open the parentheses with inversing the signs of the terms within. Also when grouping similar terms, take care of their respective signs or in order to cross check, match their respective signs (after grouping similar terms) with their respective signs in the original expression.