Transcription of 05.Equations and Inequalities (SC)
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05.Equations and Inequalities (SC)
5. EQUATIONS AND Inequalities SOLUTION OF EQUATIONS Now, we draw reference to the additive and multiplicative inverse, as it is used quite often in the solution of algebraic equations. Additive Inverse We know that 3 + -3 = 0 -8 + 8 = 0 In the first example, we refer to -3 as the additive inverse of 3 (and vice versa), and in the second example, 8 as the additive inverse of -8. We refer to zero as the Additive Identity Element. Multiplicative Inverse We know that In the first example, !" is the multiplicative inverse of 3 (and vice versa) and in the second example, 8 is the multiplicative inverse of !#. We refer to one as the Multiplicative Identity Element. Equations involving one inverse Some simple types of these types of equations are shown in the four examples below.
fractions In these examples, we may choose to eliminate the fractions using either of the following methods: Method 1 - Cross multiplication or Method 2 - Multiplying both sides by the LCM of the fractions Example 10 Solve for x: 2$ +3 5 − 3$ −1 2 = 2 Solution Method 1 – Cross multiplication Method 2 – Multiplying both sides by the LCM.
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