# Road Map #5: Equations with Special Solutions/Cross-Multiplication

May 28th, 2015
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A. Equations with Special Solutions __________Before continuing on to a couple more notes about equations, let's take a quick review of equations with variables on both sides.Problem 1: Solve: 2(t + 3) – t = 5(t – 1) + 11

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Road Map #5: Equations with Special Solutions/Cross-MultiplicationA. Equations with Special Solutions __________Before continuing on to a couple more notes about equations, let's take a quick review of equations with variables on both sides.Problem 1: Solve: 2(t + 3) t = 5(t 1) + 11Notice, in the above problem, that the numbers "dropped out," leaving us with an answer of _______________. Sometimes, the _______________ will drop out as well.Problem 2: Solve: 4(y + 3) = 3(y + 5) + y 3When we finished this problem, the variables dropped out and we got a __________ mathematical statement. When this occurs, we say that the answer to our problem is ______________________________.Problem 3: Solve each of the following equations for x:a) 1 x = x + 2b) 2(x 1) = x 2c) 3x + 2 = x + 2(x + 1)The other side of the coin involves what happens when our variables drop out and the resulting equation is _______________.Problem 4: Solve: 3(x + 1) x = 2(x 1)Clearly, we end up with a false statement. Thus, we say we have _______________.Problem 5: Solve each of the following equations for a:a) a = 1 ab) a = 1 + ac) a 1 = 1 ad) a + 1 = a ae) a a = a + af) a + 1 = 1 + ag) a + 1 = 1 ah) a 1 = a + 1i) a = 1 (1 a)B. Solving Equations Through Cross-Multiplication __________Cross-multiplication is a powerful tool that can help us solve equations.This is the official definitio

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