Beginning Algebra, 11th Edition

NOTE Remember that the variable can be isolated on either side of the equation.

In Example 2,xwill be isolated on the right if we begin by subtracting 3x.

Equation from Example 2

Subtract 3xfrom each side.

Combine like terms.

Add 8 to each side.

Combine like terms.

Divide each side by 2.

The same solution results.

There are often several equally correct ways to solve an equation.

5 = x

10

2

=

2 x

2

10 = 2 x

2 + 8 = 2 x- 8 + 8

2 = 2 x- 8

3 x+ 2 - 3 x= 5 x- 8 - 3 x

3 x+ 2 = 5 x- 8

SECTION 2.3 More on Solving Linear Equations 99

Using the Four Steps to Solve an Equation

Solve

Step 1

Multiplicative identity property

Distributive property

6 z- 3 = 3 z+ 1 Combine like terms.

8 z- 3 - 2 z= 3 z+ 1

8 z- 113 + 2 z 2 = 3 z+ 1

8 z- 13 + 2 z 2 = 3 z+ 1

8 z - 13 + 2 z 2 = 3 z +1.

EXAMPLE 4

NOW TRY
EXERCISE 3
Solve.

31 z- 62 - 5 z=- 7 z+ 7

Using the Four Steps to Solve an Equation

Solve

Step 1 Clear parentheses using the distributive property.

Distributive property

Multiply.

Combine like terms.

Step 2 Subtract k.

Combine like terms.

Add 12.

Combine like terms.

Step 3 Divide by 2.

Step 4 CHECK Original equation

Let

Work inside the parentheses.

✓ True

The solution set of the equation is 536. NOW TRY

- 3 =- 3

4102 - 3  3 - 6

413 - 32 - 3  3 - 6 k=3.

41 k- 32 - k=k- 6

k= 3

2 k

2

=

6

2

2 k= 6

2 k- 12 + 12 =- 6 + 12

2 k- 12 =- 6

3 k- 12 - k=k- 6 - k

3 k- 12 =k- 6

4 k- 12 - k=k- 6

41 k 2 + 41 - 32 - k=k- 6

41 k- 32 - k=k- 6

41 k- 32 - k= k- 6.

EXAMPLE 3

Be careful

with signs.

NOW TRY ANSWER

3. 556