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The Addition Property of Equality. § 2.2. Linear Equations. Linear equations in one variable can be written in the form ax + b = c , where a , b and c are real numbers, and a  0. Equivalent equations are equations that have the same solution. 8 + z = – 8. a.).

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§ 2.2

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The Addition Property of Equality

## § 2.2

### Linear Equations

Linear equations in one variable

can be written in the form ax + b = c,

where a, b and c are real numbers, and a 0.

Equivalent equations

are equations that have the same solution.

8 + z = – 8

a.)

8 + (– 8) + z = – 8 + – 8 Add –8 to each side.

Addition Property of Equality

Addition Property of Equality

If a, b, and c are real numbers, then

a = b and a + c = b + c

are equivalent equations.

Example:

z = – 16 Simplify both sides.

3p + (– 2p) – 11 = 2p + (– 2p) – 18Add –2p to both sides.

p – 11 + 11 = – 18 + 11 Add 11 to both sides.

Solving Equations

Example:

4p – 11 – p = 2 + 2p – 20

3p – 11 = 2p – 18(Simplify both sides.)

p – 11 = – 18 Simplify both sides.

p = – 7 Simplify both sides.

6 – 3z + 4z = – 4z + 4zAdd 4z to both sides.

6 + (– 6) + z = 0 +( – 6)Add –6 to both sides.

Solving Equations

Example:

5(3 + z) – (8z + 9) = – 4z

15 + 5z – 8z – 9 = – 4zUse distributive property.

6 – 3z = – 4zSimplify left side.

6 + z = 0 Simplify both sides.

z = – 6 Simplify both sides.

### Word Phrases as Algebraic Expressions

Example:

Write the following sentence as an equation.

The product of – 5 and – 29 gives 145.

The product of

– 5

and – 29

gives

145

In words:

Translate:

(– 5)

·

(– 29)

=

145