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Solve Linear Equations
Solve: Find the value(s) that make the equation true.
Isolate the variable.
If added, then add the opposite
If multiplied, then multiply by the reciprocal
Examples:
2x = 8
-8 = z + 1
Back to the Power Point presentation
x – 1 = 14
3 x

4 8
Solve the equation involving 2 operations
1. Isolate the variable, furthest first
a. If added, then add the opposite
b. If multiplied, then multiply by the reciprocal
We will be using the Addition Property of Equations and the Multiplication Property of Equations.
Solve and Check.
2x + 3 = 7
-4 = 5 – 3x
Solve and Check.
7
3c
 10
5
Back to the Power Point presentation
1
x  8  12
5
Solve the equation containing more then just one variable.
Solve
1. Combine like terms
2. Get just one variable
3. Isolate the variable, furthest first
a. If added, then add the opposite
b. If multiplied, then multiply by the reciprocal
Solve and Check:
5x – 7 + 2x = 8
7 = 4x + 3 – x
Solve
1. Combine like terms
2. Get just one variable
If variables are on both sides of the equation, and the opposite of one of them
3. Isolate the variable, furthest first
a. If added, then add the opposite
b. If multiplied, then multiply by the reciprocal
Solve and Check:
8x + 5 = 4x + 13
3x + 1 = 11 – x
Solve
1. Clear parentheses
2. Combine like terms
3. Get just one variable
If variables are on both sides of the equation, and the opposite of one of them
4. Isolate the variable, furthest first
a. If added, then add the opposite
b. If multiplied, then multiply by the reciprocal
Solve and Check.
6w + 2(2w + 3) = 16
5[2 – (2x – 4)] = 2(5 – 3x)
Types of solutions:
No solution, there is no value for the variable that will make the equation
true.
A unique answer, there is at least one value that makes the equation true.
Infinite number of solutions, all real numbers makes the equation true.
5=2
No Solution
solutions
x = number
Unique solution
5 = 5
Infinite number of
Solve and Check.
3(x – 4) = 3x + 5
4x – 3 = 3 – 2(3 – 2x)