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Setting Equations Equal To Zero: Alternate METHOD 1 Another Approach – using simple strategies BASIC A bit more to look at but the same concept Factor ● Factor = Factor ● Factor 3a = 3b If since we know 3 = 3 then in 3a = 3b what must be true about a & b? a must equal b and b must equal a a = b Factor ● Factor (x -2)(2x -3) = = Factor ● Factor (x -2)(x + 5) Using the same logic as the BASIC notice that both sides contain (x – 2). Think of it as the constant 3 in the basic. If the product of the two expressions are equal to each other and one factor is the same on both sides, than the other factors must be equal to each other. Therefore, 2x – 3 = x + 5 and when set equal to zero would be: -x -5 -x -5 x -8 =0 x=8 We also need to set x – 2 = 0 and solve to find the other solution + 2 +2 x=2 The solutions are {2, 8} Setting Equations Equal To Zero: Alternate METHOD 2 And yet …Another Approach – using simple strategies BASIC A bit more to look at but the same concept Factor ● Factor = Factor ● Factor 3a = 3b 3 is a common factor on both sides and we know we can divide both side by 3 and when we do we get: 3a 3 = a = b 3b 3 Factor ● Factor (x -2)(2x -3) = = Factor ● Factor (x -2)(x + 5) Using the same logic as the BASIC notice that both sides contain (x – 2). If you divide both sides by (x – 2) you would be left with 2x -3 = x + 5 Therefore, 2x – 3 = x + 5 and when set equal to zero would be: -x -5 -x -5 x -8 =0 x=8 We also need to set x – 2 = 0 and solve to find the other solution + 2 +2 x=2 The solutions are {2, 8} **BEWARE: It is important to remember with either of these Alternate METHODS that one of the solutions is eliminated by the process and must still be solved and stated as a solution.