Page 612 - Basic College Mathematics with Early Integers

S E C T I O N 8.4 I SOLVING EQUATIONS USING ADDITION AND MULTIPLICATION PROPERTIES 589

You may want to use the steps below to solve equations.

Steps for Solving an Equation

Step 1: If parentheses are present, use the distributive property.
Step 2: Combine any like terms on each side of the equation.
Step 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.
Step 4: Use the multiplication property of equality to divide both sides by the
numerical coefficient of the variable to solve for.
Step 5: Check the solution in the original equation.

Example 7 Solve: 312x - 62 + 6 = 0 PRACTICE 7
Solve: 412x - 32 + 4 = 0
Solution:

3(2x-6)+6=0

Step 1: 6x - 18 + 6 = 0 Apply the distributive property.
Step 2: 6x - 12 = 0 Combine like terms on the left side of the equation.
Step 3: 6x - 12 + 12 = 0 + 12 Add 12 to both sides.
6x = 12 Simplify.
6x 12
Step 4: = Divide both sides by 6.
6 6
x = 2 Simplify.
Check:
Step 5: 312x - 62 + 6 = 0
#
312 2 - 62 + 6 0
314 - 62 + 6 0
31-22 + 6 0
-6 + 6 0
0 0 True
The solution is 2.
Work Practice 7

Objective Writing Sentences as Equations

Next, we practice translating sentences into equations. Below are key words and
phrases that translate to an equal sign:

Key Words or Phrases Examples Symbols
equals 3 equals 2 plus 1 3 = 2 + 1

10
gives the quotient of 10 and -5 gives -2 =-2
-5
is/was 17 minus 12 is 5 17 - 12 = 5
yields 11 plus 2 yields 13 11 + 2 = 13
amounts to twice -15 amounts to -30 21-152 =-30
Answer
is equal to -24 is equal to 2 times -12 -24 = 21-122
7. 1