1.4 SOLVING LINEAR EQUATIONS

A __________ ____________ in one variable x is an equation that can be written in the form

where a and b are real numbers, and a ≠ 0.

0bax

SOLVING AN EQUATION

Solving an equation in x involves determining all values of x that result in a _________statement when substituted into the equation.

Such values are called ____________, or ________ of the equation.

EQUIVALENT EQUATIONS

Equivalent equations are two or more equations that have the same ____________________.

For example, , , and are equivalent equations because the solution

set for each is {-3}.

0124 x 124 x 3x

PROPERTIES OF EQUALITY

The addition property of equality: The same real number or algebraic expression

may be added to both sides of an equation without changing the equation’s _____________ _______.

The multiplicative property of equality: The same nonzero real number may multiply

both sides of an equation without changing the equation’s ______________ _______.

USING PROPERTIES OF EQUALITY TO SOLVE LINEAR EQUATIONS

add 3 to both sides

divide both sides by 6 (or multiply by ____ )

83x

3x 8x

306 x

x

306 x

EXAMPLE 1:

Solve and check 2954 x

STEPS FOR SOLVING A LINEAR EQUATION

_____________ the algebraic expression on each side by removing grouping symbols and combining like terms.

Collect all the _________ terms on one side and all the numbers, or constant terms, on the other side.

Isolate the __________ and solve. Check the proposed solution in the

___________ equation.

EXAMPLE 2:

Solve and Check xxxx 546122

EXAMPLE 3:

Solve and Check: 23131732 xx

EXAMPLE 4:

Solve and check:

14

5

4

3

7

5

xx

TYPES OF EQUATIONS

An equation that is true for all real numbers for which both sides are defined is called an __________.

An equation that is not an identity, but that is true for at least one real number, is called a _______________ equation.

An ________________ equation is an equation that is not true for even one real number.

EXAMPLE 5:

Solve and determine whether the equation is an identity, a conditional equation or an inconsistent equation 31474 xx

EXAMPLE 6:

Solve and determine whether the equation is an identity, a conditional equation, or an inconsistent equation. xxx 21997

Example 7:

The formula

N = 0.12x + 0.4

models the of new motorcycles sold in the United States, N, in millions, x years after 1998. When will new motorcycle sales reach 1.6 million?

Homework:

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