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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.
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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 What it means: For any numbers a, b, and c, if a = b, then ac = bc. You can multiply BOTH sides of an equation by any number and the equation will still hold true.
We all know that 3 = 3. Does 3(4) = 3? NO! But 3(4) = 3(4). The equation is still true if we multiply both sides by 4. An easy example: • 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?
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. Let’s try another example!
The two negatives will cancel each other out. The two fives will cancel each other out. (-5) (-5) x = -15 Does -(-15)/5 = 3? What do we do with negative fractions? Recall that Solve . Multiply both sides by -5.
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?
1) 4x = 24 Divide both sides by 4. 4x = 24 4 4 x = 6 Does 4(6) = 24? YES! 2) -6x = 18 Divide both sides by -6. -6y = 18 -6 -6 y = -3 Does -6(-3) = 18? YES! 2 Examples:
The two step method: Ex: 2x = 4 3 1. Multiply by 3. (3)2x = 4(3) 3 2x = 12 2. Divide by 2. 2x = 12 2 2 x = 6 The one step method: Ex: 2x = 4 3 1. Multiply by the RECIPROCAL. (3)2x = 4(3) (2) 3 (2) x = 6 A fraction times a variable:
