Beginning Algebra, 11th Edition

To solve the equation x- 5 = 2 , we used the addition property of equality.

SECTION 2.1 The Addition Property of Equality 87

Addition Property of Equality

If A, B, and Crepresent real numbers, then the equations

and

are equivalent equations.

That is, we can add the same number to each side of an equation without

changing the solution.

AB ACBC

In this property, Crepresents a real number. Any quantity that represents a real

number can be added to each side of an equation to obtain an equivalent equation.

x – 5 = 2

x – 5 + 5 = 2 + 5

FIGURE 1

NOTE Equations can be thought of in terms of a balance. Thus, adding the same

quantity to each side does not affect the balance. See FIGURE 1.

NOW TRY
EXERCISE 1
Solve .x- 13 = 4

Applying the Addition Property of Equality

Solve

Our goal is to get an equivalent equation of the form number.

Add 16 to each side.

Combine like terms.

CHECK Substitute 23 for xin the originalequation.

Original equation

Let

✓ True

Since a true statement results, 23 is the solution and is the solution set.

NOW TRY

5236

7 = 7

23 - 16  7 x=23.

x- 16 = 7

x= 23

x- 16 + 16 = 7 + 16

x- 16 = 7

x= a

x- 16 = 7.

EXAMPLE 1

NOW TRY
EXERCISE 2
Solve t-5.7=-7.2.

CAUTION The final line of the check does notgive the solution to the problem,

only a confirmation that the solution found is correct.

Applying the Addition Property of Equality

Solve

Add 2.9 to each side.

CHECK Original equation

Let

✓ True

Since a true statement results, the solution set is 5 - 3.5 6. NOW TRY

- 6.4=-6.4

- 3.5- 2.9-6.4 x=-3.5.

x- 2.9=-6.4

x=-3.5

x-2.9+2.9=-6.4+ 2.9

x-2.9=-6.4

x-2.9=-6.4.

EXAMPLE 2

NOW TRY ANSWERS

1. 5176 2. 5 - 1.5 6

7 is notthe

solution.

Our goal is

to isolate x.