This document provides step-by-step instructions for solving the algebraic expression 5(n - 3) + 31 = 6(n - 2) using the order of operations PEMDAS. It works through simplifying each term individually, combining like terms, and solving for the variable n. Following PEMDAS, it multiplies inside parentheses first, then adds and subtracts, arriving at the solution of n = -3.

1. Solving Algebraic
Expressions

2. Still using PEMDAS
O PEMDAS is going to help you with
basically EVERYTHING in Algebra. It’s the
easiest method to use, especially when
variables are involved.

3. LETS BEGIN
O 5(n – 3) + 31 = 6(n – 2)
O The best way to do this problem is to
break it into pieces
O First lets focus in on 5(n – 3) + 31

4. O Using PEMDAS we will multiply 5 by n
and negative 3
O Our product will be 5n – 15
O DON’T forget! We had a positive 31
outside the parentheses, now that we
have taken care of what is inside the
parentheses, we can add 31 by its like
term -15 .

5. O After adding -15 and 31 we come up with
a positive 16.
O Now the first part of our equation should
look like this
O 5n+16
O Next, we are going to handle the second
part of our equation

6. O 6( n – 2 )
O Once again, use PEMDAS to simplify
O 6 times n is 6n and 6 times negative 2 is a
negative 12
O So, 6n – 12 Is our simplified second
equation NOW TO PUT IT ALL
TOGETHER

7. O 5n – 15 = 6n – 12
O Bring together like terms (Add 12 (the sign
changes) to –15, and subtractive 5n from
6n to get 1n or n.)
O Our equation should now look like this
--3 = n
Therefore n = --3.