If either side of an equation contains a variable,
then the equation may be true for some values of
the variable and false for other values.
EXAMPLE: 3x + 1 = 7
To solve an equation means to find all values of
the variable that satisfy the equation (make the
equation true). These values are called solutions
A linear equation in the single variable x is an
equation that can be written in the form
ax + b = 0
where a and b are real numbers, with a ≠ 0.
Equivalent Equations are equations that have
exactly the same solution(s).
Example: 3x – 5 = 16
3x = 21
x = 7
Solving Linear Equations
1. List any restrictions on the domain of the variable.
2. Create Equivalent Equations.
A. Clear the fractions by multiplying both sides of the equation
by the LCD.
B. Simplify each SIDE of the equation.
a) Distribute to eliminate the parentheses.
b) Combine Like Terms.
C. Collect all variable terms on one side of the equation.
Add/subtract variable terms to each side of equation.
D. Collect all numbers on the other side of the equation.
Add/subtract numbers to each side of equation.
E. Isolate the variable. This is the solution.
Multiply/divide by the variable coefficient.
3. Check your solution(s) in the domain.
Solve the equation: x 1 3 3x 2
Solve the equation: 3x 1 x 2 x 33x 2
2 3 1
Solve the equation:
x 1 x 3 x 3 x 1
Equations, And Identities
• An equation that has NO SOLUTION is called a
• An equation that is true for some values of the
variable and not for others is called a conditional
• An identity is an equation that is true for every value
of the variable.
Examples: 3x – ½ = 18
3(x – 9) = 3x – 27
Solve the equation: 1
Solving for a Variable in a