Download Solving Equations with Variables on Both Sides

Math I: Unit 1
Steps to Solving Equations with
Variables on Both Sides
Step 1: Simplify Both Sides, if possible
Distribute
Combine like terms
Example Problem:
3( 2 x  5)  4 x  13  3 x  8
Step 2: Move the variable to one side
Add or Subtract Like Term
Step 3: Solve for the variable
Use opposite operations to cancel
numbers
Ex 1
Ex 3
3 x  12  14  5 x
4( 2 y  4)  5 y  2
Ex 2
 4 x  16  22  7 x
Ex 4
4 x  19  3  3( x  3)
Types of Solutions
• ONE Solution
There is only one answer that makes the equation true
(EX: x=3 This is the answer)
• NO Solution
There is no number that will satisfies both sides of the
equation. Variables will cancel and a false statement is left.
(EX: 5=3 Answer: No solution)
• MANY Solutions
Any number substituted for the variable will make the
equation true. All variables will cancel and a true
statement will be left.
(EX: -2=-2 Answer: All real numbers)
Practice: Solve each equation.
#1
8 5y  7 2y
#3
2m  5  5m  35  3m
#2
2(9 x  8)  3(6 x  2)
#4
3  ( 2 x  1)  ( 3 x  6)  x  10