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1.4 SOLVING LINEAR EQUATIONS A __________ ____________ in one variable x is an equation that can be written in the form ax b 0 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 x 3 are equivalent equations because the solution set for each is {-3}. 4x 12 0 , 4 x 12 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 x 3 8 add 3 to both sides x 3 x 8 6x 30 divide both sides by 6 (or multiply by ____ ) 6x 30 x EXAMPLE 1: Solve and check 4x 5 29 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 2x 12 x 6x 4 5x EXAMPLE 3: Solve and Check: 2x 3 17 13 3x 2 EXAMPLE 4: Solve and check: x 5 x 3 5 7 4 14 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 4x 7 4x 1 3 EXAMPLE 6: Solve and determine whether the equation is an identity, a conditional equation, or an inconsistent equation. 7 x 9 9x 1 2 x 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: Page 46 1 – 49 odds 25 total