1.4 S OLVING L INEAR E QUATIONS 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.

S OLVING AN E QUATION 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.

E QUIVALENT E QUATIONS 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}.

P ROPERTIES 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 ______________ _______.

U SING P ROPERTIES OF E QUALITY TO S OLVE L INEAR E QUATIONS add 3 to both sides divide both sides by 6 (or multiply by ____ )

E XAMPLE 1: Solve and check

S TEPS FOR S OLVING A L INEAR E QUATION _____________ 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.

E XAMPLE 2: Solve and Check

E XAMPLE 3: Solve and Check:

E XAMPLE 4: Solve and check:

T YPES OF E QUATIONS 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.

E XAMPLE 5: Solve and determine whether the equation is an identity, a conditional equation or an inconsistent equation

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

Example 7: The formula N = 0.12x models the of new motorcycles sold in the United States, N, in millions, x years after When will new motorcycle sales reach 1.6 million?

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