Solve Equations with Division Quickly and Easily

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Solve Equations with Division

Now that you have learned the addition method, let's learn how to solve equations with division.

The process is similar, so let's get to it.

Example #1:

Solve 2x = 4

Please notice that in this type of problem, we only have one term on each side of the equation. 2x is on the left side, and 4 is on the right side. We don't have any numbers being added or subtracted.

2	x	=	4	original equation
2 2	x	=	4 2	divide both sides by 2
	x	=	2	simplify both sides (answer)

Let's Think Logically about 2x = 4. Remember, x is a variable - it represents something. Let's imagine it represents a cheeseburger.

solve equations with burgers

Instead of 2x = 4, we now have 2 burgers costing $4.

cheeseburgers cost $$$ If you can buy 2 burgers for $4, how much does 1 burger cost you?

Think about it!

I'm sure you realize that each burger costs $2. When you solve equations with division, this is all we need to do. Now sometimes, it will be easy for you to go right to the answer, and other times you will need to rely on your math skills. Let's look at some more examples.

Example #2: Solve 6x = 18

You might already know the answer, but let's look at how to do it:

6	x	=	18	original equation
6 6	x	=	18 6	divide both sides by 6
	x	=	3	simplify both sides (answer)

"If 6 burgers cost $18, that means that 1 burger cost $3"

Example #3: Solve ⅓x = 4

Up until now we've learned to solve equations with division. This time we are going to solve using multiplication. The idea is very similar, so don't worry. Remember, always do the opposite operation. A fraction is like division, so we must use the opposite - multiplication!

	1 3	x	=	4	original equation
3¡¤	1 3	x	=	3¡¤4	multiply both sides by 3
. .	1	x	=	12	simplify both sides
.		x	=	12	1x is the same as x

"If one-third of a burgers cost $4, the whole thing costs $12"

Cheeseburger Anyone?

Is learning how to solve equations with division making you hungry for more great algebra help lessons?

(ok, sorry ... we got carried away)

Think you're as smart as Alex Trebek? Check out Math Jeopardy at GradeA's math games, or browse other free math help section: homepage.

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