2-3 Solving Equations Using Multiplication and Division Indicators: NS4, PA5, PA7, PA8  Created by: Edited by Eddie Judd, Crestwood Middle School

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: 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? 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.

Let’s try another example! 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. x = 4 2 Multiply each side by 2. (2)x = 4(2) x = 8

What do we do with negative fractions? The two negatives will cancel each other out. The two fives will cancel each other out. (-5) (-5) x = -15 Does -(-15)/5 = 3? 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?

2 Examples: 1) 4x = 24 Divide both sides by 4. 4x = 24 4 4 x = 6 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!

A fraction times a variable: The two step method: Ex: 2x = 4 3 1. Multiply by 3. (3)2x = 4(3) 2x = 12 2. Divide by 2. 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

Try these on your own...

The answers...