Page 630 - Basic College Mathematics with Early Integers

CHAPTER HIGHLIGHTS 607

Definitions and Concepts Examples

Section 8.1 Variable Expressions (continued)

Use the distributive property to multiply an algebraic Simplify:
expression by a term.
-41x + 22 + 315x - 72
=-41x2 + 1-42122 + 315x2 - 3172
=-4x + 1-82 + 15x - 1212
=-4x + 15x + 1-82 + 1-212
= 11x + 1-292 or 11x - 29

Section 8.2 Solving Equations: The Addition Property

ADDITION PROPERTY OF EQUALITY Solve for x:
Let a, b, and c represent numbers.Then x + 8 = 2 + 1-12
a = b Also, a = b x + 8 = 1
and a + c = b + c and a - c = b - c x + 8 - 8 = 1 - 8 Subtract 8 from both sides.
are equivalent equations. are equivalent equations. x =-7 Simplify.
In other words, the same number may be added to or sub- The solution is -7.
tracted from both sides of an equation without changing
the solution of the equation.

Section 8.3 Solving Equations: The Multiplication Property

MULTIPLICATION PROPERTY OF EQUALITY Solve: -7x = 42
-7x 42
Let a, b, and c represent numbers and let c Z 0. then = Divide both sides by -7.
-7 -7
a = b Also, a = b x =-6 Simplify.
a b
#
#
and a c = b c and = 2
c c Solve: x =-10
3
are equivalent equations. are equivalent equations.
1 1
In other words, both sides of an equation may be multi- 3 # 2 x = 3 # -10 Multiply both sides by .
3
plied or divided by the same nonzero number without 2 3 2 2
1 1
changing the solution of the equation.
x =-15 Simplify.
Section 8.4 Solving Equations Using Addition and Multiplication Properties

STEPS FOR SOLVING AN EQUATION Solve for x: 5(3x-1)+15=–5
Step 1. If parentheses are present, use the distributive
Step 1. 15x - 5 + 15 =-5 Apply the distributive
property.
property.
Step 2. Combine any like terms on each side of the
Step 2. 15x + 10 =-5 Combine like terms.
equation.
Step 3. 15x + 10 - 10 =-5 - 10 Subtract 10 from both
Step 3. Use the addition property of equality to rewrite
sides.
the equation so that variable terms are on one
15x =-15
side of the equation and constant terms are on
the other side. Step 4. 15x = -15 Divide both sides
Step 4. Use the multiplication property of equality to 15 15 by 15.
divide both sides by the numerical coefficient of x =-1
the variable to solve. Step 5. Check to see that -1 is the solution.
Step 5. Check the solution in the original equation.