Solving Equations Using Multiplication and Division

Solve linear equations in one variable. Apply these skills to solve practical

problems. Justify steps used in solving equations.

Objectives:

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.

Does 3(4) = 3? NO!

But 3(4) = 3(4).

The equation is still true if we multiply both sides by 4.

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?

Let’s try another example!

x = 4 2Multiply each

side by 2.(2)x = 4(2) 2x = 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.

x

5

x5

x

5

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.

x5

3 x5

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

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 31. Multiply by 3.(3)2x = 4(3) 32x = 12

2. Divide by 2.2x = 12 2 2x = 6

The one step method:Ex: 2x = 4 31. Multiply by the

RECIPROCAL.

(3)2x = 4(3)(2) 3 (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