Basic Mathematics for College Students

When solving an equation, if variables appear on both sides, we can use the

addition (or subtraction) property of equality to get all variable terms on one side and

all constant terms on the other.

672 Chapter 8 An Introduction to Algebra

Self Check 6

Solve:

Now TryProblem 57

30  6 n 4 n 2

Do the subtractions. Now we want to isolate the variable, a.

On the left side, simplify:.

On the right side, do the division.

The solution is 9. Use a check to verify this.

6

1

a

a 9 61 a^

To undo the multiplication by 6, divide both sides by 6.

(^) This isolates a.
6 a
6



54

6

6 a 54

EXAMPLE (^6) Solve:
StrategyThere are variable terms and on both sides of the equation. We
will eliminate from the left side of the equation by subtracting from both
sides.
WHYTo solve for , all the terms containing must be on the same side of the
equation.
Solution
Do the subtractions.
Check: This is the original equation.
Substitute 51 for x.
Do the multiplications.
True
The solution is  51.

 168  168

 153  15  204  36

3( 51 ) 15 4( 51 ) 36

3 x 15  4 x 36

 51 x

To undo the addition of 36, subtract

 15  36 x 36  (^36) 36 from both sides. This isolates x.
Combine like terms: 3x 3 x0 and 4x 3 xx.
 15 x (^36) Now we want to isolate the variable, x.
Subtract 3xfrom both sides to isolate the variable
3 x 15  3 x 4 x 36  3 x term on the right side.
This is the equation to solve. There are variable
3 x 15  4 x (^36) terms on both sides of the equation.
x x
3 x 3 x
(3x 4 x)
3 x 15  4 x 36
Success Tip In Example 6, we could have eliminated from the right side
by subtracting from both sides:
Note that the coefficient of xis negative.
However, it is usually easier to isolate the variable term on the side that will
result in a positivecoefficient.
x 15  36
3 x 15  4 x 4 x 36  4 x
4 x
4 x
EXAMPLE (^7) Solve: 3(4x80)  6 x2(x40)
StrategyWe will use the distributive property on each side of the equation to
remove the parentheses. Then we will combine any like terms.
WHYIt is easiest to simplify the expressions that make up the left and right sides
of the equation before using the properties of equality to isolate the variable.
1
1
5
 36
51
9
2
1
0
10
4
14
 36
168
153
 15
168
51
 4
204
51
 3
153
Self Check 7
Solve:
6(5x– 30) – 2x= 8(x+ 50)
Now TryProblem 59