1 4 SOLVING LINEAR EQUATIONS A in one

SOLVING AN EQUATION Solving an equation in x involves determining all values of x

EQUIVALENT EQUATIONS Equivalent equations are two or more equations that have the same __________.

PROPERTIES OF EQUALITY The addition property of equality: The same real number or algebraic

USING PROPERTIES OF EQUALITY TO SOLVE LINEAR EQUATIONS add 3 to both sides divide

STEPS FOR SOLVING A LINEAR EQUATION _______ the algebraic expression on each side by

TYPES OF EQUATIONS An equation that is true for all real numbers for which

EXAMPLE 5: Solve and determine whether the equation is an identity, a conditional equation

EXAMPLE 6: Solve and determine whether the equation is an identity, a conditional equation,

EXAMPLE 7: The formula N = 0. 12 x + 0. 4 models the

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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.

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}.

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 ____ )

EXAMPLE 1: Solve and check

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

EXAMPLE 3: Solve and Check:

EXAMPLE 4: Solve and check:

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

EXAMPLE 6: Solve and determine whether the equation is an identity, a conditional equation, or an inconsistent equation.

EXAMPLE 7: The formula N = 0. 12 x + 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?

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