Mini-Lecture 1.1
Linear Equations
1. Determine whether a number is a solution to an equation.
2. Solve linear equations.
3. Determine whether an equation is a conditional equation, identity, or contradiction.
Preparing for Linear Equations:
i) Find the LCD of
5
6
and
3
4
. ii
) Simplify:
3(2 5) 12 8
x x
− − − −
Examples:
1. Determine which of the numbers are solutions to:
4 8 7( 1)
t t
− = +
.
a) t = 5 b) t = 3
c) t = −15 d) t = −5
STEPS FOR SOLVING A LINEAR EQUATION
Step 1: Remove any parentheses using the Distributive Property.
Step 2: Combine like terms on each side of the equation.
Step 3: Use the Addition Property of Equality to get all variables on one side of the equation and all constants on the
other side.
Step 4: Use the Multiplication Property of Equality to get the coefficient of the variable to equal .
Step 5: Check your answer to be sure that it satisfies the original equation.
