1. Equation with variables on both sides

2. Introduction What is an equation?
An equation is a mathematical statement that
shows 2 quantities are equal. An equation contains
an equal sign.
12 – 3 = 9 Numerical
3a = 30 Algebraic

3. Steps for Solving One-Step Equations
1) Get the variable on one side of the equation.
2) You always perform the same operation to
both sides of an equation.
3) To undo an operation you perform its opposite
operation to both sides of the equation.

4. Opposite operations
The opposite of add is
SUBTRACT
ADD
The opposite of subtract is
The opposite of multiply is
DIVIDE
MULTIPLY
The opposite of divide is

5. Solving Equations Using Addition or Subtraction:
Rule 1: If a number has been added to the variable, subtract that number from both sides of the equation. Rule 2: If a number has been subtracted from the variable, add that number to both sides of the equation.

6. Solving Equations Using Multiplication or Division
Rule 3: If a variable has been multiplied by a non zero number, divide both sides by that number. Rule 4: If a variable has been divided by a number, multiply both sides by that number.

7. = 3x + 7 x + 15 3x + 7 = 15 + x = = = 3x + 7 - 7 x + 15 - 7 3x x + 8
Example 1: Solve 3x + 7 = x + 15
Solution:
Equals = 3x
x + 15
RHS
LHS
3x + 7 = x
Variable/
Unknown
Variable/
Unknown
Constants
Get the variable on one side of the equation.
We keep variable x on the Left Handside(LHS) and move constant to the Right Handside(RHS)
By rule 1, 7 is added to the
variable, so subtract 7 from
both sides of the equation 3x = x 3x =
x + 8
To remove x on RHS,
subtract x from both sides
of the equation
By integer rule, if numbers
have different sign,
subtract the numbers and put sign of bigger number
3x - x =
x x

8. 2x = = Continue 8 2 x x 8 Ans: x = 4 By rule 3, a variable is
We keep variable x on the Left
Handside(LHS) and move constant to
the Right Handside(RHS)
2 x x = 8
By rule 3, a variable is
multiplied by 2, so divide
both sides by 2
x = 4
Ans: x = 4

9. Example 2: Solve 20 – 4x = 8x + 8
Solution:
Equals =
20 – 4x
8x + 8
RHS
LHS
20 – 4x =
8x + 8
Constants
Constants
Variable/Unknown
Get the variable on one side of the equation.
We keep variable x on the Right Handside(RHS) and move constant to the Left Handside(LHS)
By rule 1, 8 is added to the
variable 8x , so subtract 8 from
both sides of the equation
x - 8 = 8x
-4x + 12 = 8x
To remove 4x on LHS
add 4x to both sides
of the equation
By integer rule, if numbers
have different sign,
subtract the numbers and put sign of bigger number
- 4x x =
8x + 4x

10. 12 = = Continue 12x 12 12 x x Ans: x = 1 By rule 3, a variable is
We keep variable x on the Left
Handside(LHS) and move constant to
the Right Handside(RHS) 12 =
12 x x
By rule 3, a variable is
multiplied by 12, so divide
both sides by 12
1 = x
Ans: x = 1

11. Try These
Solve the following
15 + 6x = x
5x + 20 = 6x - 5