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2-Step Equations What??? I just learned 1-step! Relax. You’ll use what you already know to solve 2-step equations. Solving Two-Step Equations To find the solution to an equation we must isolate the variable. In other words, get the variable on one side of the equation by itself. We isolate the variable by performing operations that will eliminate (cancel) the other numbers from the expression. Solving Two-Step Equations We have seen how to eliminate a constant (Addition Property of Equality) & how to eliminate a coefficient (Multiplication Property of Equality). What if an equation has both a constant and a coefficient to be eliminated? This is called a Two-Step Equation. STEP 1 The first step will always be either adding or subtracting. (Think: Order of Operations backwards) STEP 2 The second step will always be either multiplying or dividing. EX1) 8x + 5 = 61 -5 -5 This problem has multiplication, so we need to divide now. 8x = 8 x = 56 8 7 This problem has addition, so we need to subtract first. Whatever we do on one side, we have to do on the other. Check 8x + 5 = 61 8(7) + 5 = 61 56+ 5 = 61 61= 61 EX2) 3a - 8 = 4 +8 +8 This problem has multiplication, so we need to divide now. 3a = 3 a = 12 3 4 This problem has subtraction, so we need to add first. Check 3a - 8 = 4 3(4) - 8 = 4 12 - 8 = 4 4= 4 EX3) z + 2 = 26 6 -2 -2 z 6• 6 This problem has division, so we need to multiply now. = z This problem has addition, so we need to subtract first. 24 • 6 = 144 Check z + 2 = 26 6 144 + 2 = 26 6 24 + 2 = 26 26 = 26 EX4) m - 10 = 15 5 +10 +10 m 5• 5 This problem has division, so we need to multiply now. = 25 • 5 m = 125 This problem has subtraction, so we need to add first. Check m - 10 = 15 5 125 - 10 = 15 5 25 - 10 = 15 15= 15 Assignment Page 537 1-6 , 9-11 show work on a separate sheet of paper Notes start here Date ______________ 2-Step Equations EX1) 8x + 5 = 61 EX2) 3a - 8 = 4 EX3) z + 2 = 26 6 EX4) m - 10 = 15 5