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Solving Equations Using Multiplication and Division Objectives: Solve linear equations in one variable. Apply these skills to solve practical problems. Justify steps used in solving equations. Remember, To Solve an Equation means... To isolate the variable having a coefficient of 1 on one side of the equation. Ex: x = 5 is solved for x. y = 2x - 1 is solved for y. Multiplication Property of Equality For any numbers a, b, and c, if a = b, then ac = bc. What it means: You can multiply BOTH sides of an equation by any number and the equation will still hold true. An easy example: We all know that 3 = 3. Would you ever put deodorant under just one arm? Would you ever put nail polish on just one hand? Would you ever wear just one sock? Does 3(4) = 3? NO! But 3(4) = 3(4). The equation is still true if we multiply both sides by 4. Let’s try another example! x=4 2 Multiply each side by 2. (2)x = 4(2) 2 x=8 Always check your solution!! The original problem is x=4 2 Using the solution x = 8, Is x/2 = 4? YES! 4 = 4 and our solution is correct. What do we do with negative fractions? Recall that x x x 5 5 5 x 3. Solve 5 Multiply both sides by -5. The two negatives will cancel each other out. The two fives will x canceleach 3 other out.5 (-5) (-5) x = -15 Does -(-15)/5 = 3? Division Property of Equality For any numbers a, b, and c (c ≠ 0), if a = b, then a/c = b/c What it means: You can divide BOTH sides of an equation by any number - except zero- and the equation will still hold true. Why did we add c ≠ 0? 2 Examples: 1) 4x = 24 Divide both sides by 4. 4x = 24 4 4 2) -6x = 18 Divide both sides by -6. -6y = 18 -6 -6 x=6 Does 4(6) = 24? YES! y = -3 Does -6(-3) = 18? YES! A fraction times a variable: The two step method: Ex: 2x = 4 3 1. Multiply by 3. (3)2x = 4(3) 3 2x = 12 The one step method: Ex: 2x = 4 3 1. Multiply by the RECIPROCAL. (3)2x = 4(3) (2) 3 (2) x=6 2. Divide by 2. 2x = 12 2 2 x=6 Try these on your own... x=3 7 4w = 16 y=8 -2 2x = 12 3 -2z = -12 3x = 9 -4 The answers... x = 21 w= 4 y = -16 x = 18 z=6 x = -12