Download Chapter 2

§ 2.4
Solving Linear
Equations with a
Variable on One Side of
the Equation
Equations with a Variable on One Side
1.
2.
3.
4.
5.
6.
If the equation contains fractions, multiply both
sides by the LCD to eliminate fractions.
Use the distributive property to remove
parentheses.
Combine like terms on the same side of the equal
sign.
Use the addition property to obtain an equation in
the form ax = b.
Use the multiplication property to isolate the
variable.
Check the solution in the original equation.
Angel, Elementary Algebra, 7ed
2
Solving Equations
Example: Solve the equation 3(4 – x) + 5x = 9.
12 – 3x + 5x = 9
(Distributive property)
12 + 2x = 9
(Combine like terms.)
12 - 12 + 2x = 9 - 12 (Add –12 to both sides.)
2x = -3
(Divide both sides by 2.)
x 3
2
Don’t forget to check!
Angel, Elementary Algebra, 7ed
3
Solving Equations with Fractions
Example: Solve the equation 45 n  13 .
15(4 n) 151
5
3
3
5
4
15( )15n 151
51
31
12 + 15n = 5
15n = -7
n = -7/15
(Multiply by the LCD, 15.)
(Distribute.)
(Simplify.)
(Add –12 to both sides.)
(Divide both sides by 15.)
Angel, Elementary Algebra, 7ed
4
Helpful Hints and Definitions



To evaluate an expression means to find its
numerical value.
To simplify an expression means to perform
operations and combine like terms.
To solve an equation means to find the value of the
variable that makes the equation a true statement.
Angel, Elementary Algebra, 7ed
5