Beginning Algebra, 11th Edition

CHAPTER 2 Summary^165

2.1 The Addition Property of Equality

The same number may be added to (or subtracted from)
each side of an equation without changing the solution.

Solve.

Add 6.

Combine like terms.

Solution set: 5186

x= 18

x- 6 + 6 = 12 + 6

x- 6 = 12

QUICK REVIEW

CONCEPTS EXAMPLES

2.2 The Multiplication Property of Equality

Each side of an equation may be multiplied (or divided)
by the same nonzero number without changing the
solution.

Solve.

Multiply by

Solution set: 5 - 126

x=- 12

4

3.

4

3

#a^3

4

xb=

4

3

1 - 92

3

4

x=- 9

2.3 More on Solving Linear Equations

Step 1 Simplify each side separately.

Step 2 Isolate the variable term on one side.

Step 3 Isolate the variable.

Step 4 Check.

Solve.

Distributive property

Combine like terms.

Subtract x. Subtract 2.

Combine like terms.

Divide by 3.

CHECK Let

✓ True

Solution set: 546

18 = 18

2142 + 214 + 12  14 + 4 x=4.

x= 4

3 x

3

=

12

3

3 x= 12

4 x+ 2 - x- 2 = 14 +x-x- 2

4 x+ 2 = 14 +x

2 x+ 2 x+ 2 = 14 +x

2 x+ 21 x+ 12 = 14 +x

2.4 An Introduction to Applications

of Linear Equations

Step 1 Read.

Step 2 Assign a variable.

Step 3 Write an equation.

Step 4 Solve the equation.

Step 5 State the answer.

Step 6 Check.

One number is five more than another. Their sum is 21. What are the

numbers?

Let x the lesser number.

Then the greater number.

Combine like terms.

Subtract 5.

Divide by 2.

The numbers are 8 and 13.

13 is five more than 8, and 8 + 13 =21. It checks.

x= 8

2 x= 16

2 x+ 5 = 21

x+ 1 x+ 52 = 21

x+ 5 =

=

(continued)