Download Solving Equations Using the Addition and Multiplication Properties

Math 64
3.3 "Solving Linear Equations in One Variable"
Objectives:
*
Solve linear equations.
*
Write numerical sentences as equations.
Solving Equations Using the Addition and Multiplication Properties
In this chapter, the equations we are solving are called linear equations in one variable or …rst-degree equations
in one variable. For example, an equation such as 5x 2 = 6x is a linear equation in one variable. It is called linear
or …rst degree because the exponent on each x is 1 and there is no variable below a fraction bar. It is an equation in one
variable because it contains one variable, x:
Steps for Solving an Equation:
1: If parentheses are present, use the distributive property.
2: Combine any like terms on each side of the equation.
3: Use the addition property of equality to rewrite the equation so that variable terms are on
one side of the equation and constant terms are on the other side.
4: Use the multiplication property of equality to divide both sides by the numerical coe¢ cient
of the variable to solve.
5: Check the solution in the original equation.
Example 1: (Solving equations)
Solve:
a) 7x + 12 = 3x
c)
9 + 20 = 19x
4
4
18x
b) 19x
2
d) 6 (a
5) = 4a + 4
Page: 1
7x = 31 + 6x
15
Notes by Bibiana Lopez
Prealgebra by Elayn Martin-Gay
3.3
e) 12 + 5t = 6 (t + 2)
f) 14 + 4 (m
5) = 6
2m
Writing Numerical Sentences as Equations
Example 2: (Writing numerical sentences as equations)
Translate each sentence into an equation.
a) The di¤erence of 110 and 80 is 30.
b) The product of 3 and the sum of
9 and 11 amounts to 6.
c) The quotient of 24 and
4:
6 yields
Page: 2
Notes by Bibiana Lopez