Basic Mathematics for College Students

The Language of Algebra In Example 1, we subtract 5 from both sides to

isolate the variable term, 12 x.Then we divide both sides by 12 to isolate the

variable,x.

8.4 More about Solving Equations 669

Check: This is the original equation.

Substitute 1 for.

Do the multiplication on the left side.

True

The solution is 1.

Caution! When checking solutions, always use the original equation.

17  17

12  5  17

12( 1 ) 5  17 x

12 x 5  17

EXAMPLE (^2) Solve: 10  5 s 60
StrategyFirst we will use a property of equality to isolate the variable termon
one side of the equation.Then we will use a second property of equality to isolate
the variableitself.
WHYTo solve the original equation, we want to find a simpler equivalent
equation of the form a numbers, whose solution is obvious.
Solution
On the right side of the equation, 5 is multiplied by 5, and then 60 is subtracted
from that product. To isolate s, we undo the operations in the opposite order.

• To isolate the variable term, 5 s, we add 60 to both sides to undo the
  subtraction of 60.


• To isolate the variable,s, we divide both sides by 5 to undo the
  multiplication by 5.

10  60

10  60  5 s 60  60

70  5

 14 s

On the right side, simplify:

Check: 10  5 s 60 This is the original equation.

10 5( 14 )  60 Substitute 14 for s.

10  70  60 Do the multiplication on the right side.

10  10 True

The solution is –14.

 5

1

s

 15 s.

On the left side, do the division. The quotient

of a positive and a negative number is negative.

Use the division property of equality:

Divide both sides by 5 to isolate s.

70

 5



 5 s

 5

Do the additions: 10  60 70 and  60  60 0.

s Now we want to isolate the variable, s.

Use the addition property of equality: Add 60 to

both sides to isolate  5 s.

This is the equation to solve. First, we

 5 s want to isolate the variable term,  5 s.

14

(^5)  70
 5
20
 20
0
Self Check 2
Solve: 40 4 d 8
Now TryProblem 25
1
2
4
 5
70