Learning Outcomes
• Solvemulti-step linear equations in one variable
with rational coefficients
• Solve linear equations whose solutions require
expanding expressions and collecting like terms
3.
Linear Equations
Linear equationsin one variable are in the form:
A x + b = 0
A = coefficient, x = variable, b = constant term
In order to solve equations in one variable, you need to isolate the variable on one
side with constants on the other side. Mathematical operations must be performed
to both sides of the equal sign in order to isolate the variable and keep the equation
balanced.
Linear Equations
No Solutions
5x- 8 = 5x + 2
- 8 = 2
- 5x
No Solution
Below is an example of a linear equation that has no solution. There are no values of x
that would satisfy the equation and their graphs would be parallel.
- 5x
6.
Linear Equations
Infinite Solutions
3x- 1 = -1 + 3x
-1 = -1
-3x
Infinite Solution
-3x
Below is an example of a linear equation that has infinite solutions. Their graphs would
have the same slope and intercept, therefore they would have infinite solutions.
7.
Two Step Equations
Examples
Solvethe following two step equations:
3x + 4 = - 17
3x = - 21
x = - 7
-4 -4
÷ 3 ÷ 3
a) 6 - 5x = -19
-5x = - 25
x = 5
-6 -6
÷ -5 ÷ -5
b)
8.
Equations with Brackets
Solvethe following equations with brackets:
4x - 12 = -6
4x = 6
x = 1.5
+12 +12
÷ 4 ÷ 4
5x = -10
x = -2
÷ 5
÷ 5
4(x - 3) = -6
a) 2(x - 3) + 3(x + 1) = -13
b)
2x - 6 + 3x + 3 = -13
5x - 3 = -13
+3
+3
Examples
9.
Equations with Unknownson Both
Sides
Solve the following equations with unknowns on both sides:
18 = 12x
x = 1.5
÷ 12
÷ 12
a) 12 - 8x = 4x - 6
b)
12 = 12x - 6
+6
+6
Examples
x = 9
3x - 5 = 2x + 4
x - 5 = 4
+5
+5
-2x -2x +8x +8x
