Basic Mathematics for College Students

8.4 More about Solving Equations 673

20

(^16)  320
 32
00
 0
0

1. 7 2. 12 3. 36 4.3.9 5. a. 1 b. 11 6. 16 7. 29

ANSWERS TO SELF CHECKS

Fill in the blanks.

1. To an equation means to find all values of the
   variable that make the equation true.

VOCABULARY 2. The equation 6x 3  4 x1 has variable terms on

sides.

3. When solving equations, the expressions that
   make up the left and right sides of the equation before
   using the properties of equality to isolate the variable.

SECTION 8.4 STUDY SET

Solution

3(4x80)  6 x2(x40) This is the equation to solve.

12 x 240  6 x 2 x 80 Distribute the multiplication by 3 and by 2.

18 x 240  2 x 80

18 x 240  2 x 2 x 80  2 x

16 x 240  80

16 x 240  240  80  240

16 x 320

x 20

On the left side, simplify,

On the right side, do the division.

The solution is 20. Check by substituting it in the original equation.

16

1

x

161 x.

To isolate x on the left side,

divide both sides by 16 to undo

the multiplication by 16.

16 x

16



320

16

Do the addition on each side:

 240  240 0 and 80  240 320.

Now we want to isolate the variable, x.

To isolate the variable term, 16x,on

the left side, add 240 to both sides

to undo the subtraction of 240.

Combine like terms on each side:

18 x 2 x 16 xand 2x 2 x0.

To eliminate the term 2xon the right

side, subtract 2xfrom both sides.

On the left side, combine like terms:

12 x 6 x 18 x. There are variable

terms on both sides.

The previous examples suggest the following strategy for solving equations. You
won’t always have to use all four steps to solve a given equation. If a step doesn’t
apply, skip it and go to the next step.

Stategy for Solving Equations

1.Simplify each side of the equation:Use the distributive property to remove

parentheses, and then combine like terms on each side.

2.Isolate the variable term on one side:Add (or subtract) to get the variable

term on one side of the equation and a number on the other using the

addition (or subtraction) property of equality.

3.Isolate the variable:Multiply (or divide) to isolate the variable using the

multiplication (or division) property of equality.

4.Check the result:Substitute the possible solution for the variable in the

original equation to see if a true statement results.

2

1

40

 80

320