How To Solve Equations With Variables On Both Sides

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TREVOR HUNT HA FOOLED YOU Say you have the problem 6x + 7 = 12x - 5 The easiest way to solve these problems is to get x onto one side. To get x on one side you would either subtract 6x from each side or subtract 12x from each side. It would be easier to subtract 6x so we have all positive numbers. So if you subtract 6x from each side it would look like this: 6x + 7 = 12x - 5

-6x -6x

You would have 7 = 6x - 5 Now you would have to add 5 because you want to get x alone. You can also subtract 7. The easier way to do it would be to add 5. So you have the equation 7 = 6x - 5 and you would have to add five to each side : 7 = 6x - 5

+5 +5

Now you would have 12 = 6x Now you need to simplify it. You would have to divide to simplify the new equation 12 = 6x, so divide by six to get x all by itself. So you have 12 = 6x and you need to divide both sides of the equation by 6. It should look like this: 12/6 = (6x)/6 to get 2 = x. Let's do another example. Say you have 4x = 4x + 5. Again, you have to get x alone and on one side. So you would have to subtract 4x. So it would look like this: 4x = 4x + 5

-4x -4x

You would get 0 = 5. As you know zero does not equal five, so this type of equation is one that has "no solution" meaning whatever the x value is, the equation would not be correct. The right way to write this would be 0 ≠ 5. Meaning zero does not equal five. Now let's do word problems! Problem 1: Uniforms:

The boy's basketball team needs shirts for their season. Tom's T's charges a set up fee for the graphics of $50.00 per order and $15.00 per shirt. Sam's Shirts has no set up fee but charges $20.00 a shirt. What number of uniforms would have to be bought so the total price would be the same at each store? At Tom's "T's", they are charging $15.00 per shirt with an ADDITIONAL charge for the set up fee of $50.00. Let's use x as our variable. $15.00 PER shirt. Meaning every shirt you buy. You don't know how many you will buy, so to set this up it will be 15x. Then you have the set up fee of $50.00. It's just an additional fee. That will just be 15x + 50. Sam's Shirts charges $20.00 per shirt with no additional charge. This would be 20x. So to put this into an equation, your equation will be (Tom's T's) = (Sam's shirts.)

15x + 50 = 20x

This is your equation. To solve this problem, you need to simplify the equation so that you have the amount of shirts that the total price for each store is equal.

15x + 50 = 20x

Let's start off by making the equation as easy as possible by subtracting 15x from both sides.

15x + 50 = 20x

-15x -15x

50 = 5x

Now you want to divide to get x alone on one side.

50/5 = 5x/5

10 = x <----- This is the most you can simplify.

It is saying that if you want to buy ten uniforms, it doesn't matter what store you buy from. The total price is the same. If you want to buy fewer then ten uniforms, you should probably buy from Sam's Shirts. More, Tom's T's. Problem 2: Shoes:

Players made the Eastbay Middle School Basketball Team. Nike sells shoes for $115.00 a pair without a discount. Adidas sells basketball shoes for $125.00 a pair with a discount of $10.00 per pair of shoes. How many shoes can be bought to get the same price at each store? Nike sells shoes for $115.00 per pair with no discount. If you don't know how many pairs of shoes you are buying, and you use x as a variable, it would be 115x. Adidas sells shoes for $125.00 a pair with a $10.00 discount per pair. So your equation would be:

115x = 125x - 10x Now you need to simplify again. If you have

125x - 10x, you can combine them. If two numbers have the same variables, they are called like terms, and you can combine like terms.

115x = 125x - 10x. <--- You can combine these. You would get:

115x = 115x

Now I hope you can see something. The coefficient and variable are the same on both sides. It means what ever the x value is, the price is going to be the same at both stores. You would have to divide by 115 to get x alone.

(115x)/115 = (115x)/115

x = x

It wouldn't matter which store you bought shoes from because regardless of how many shoes you buy, the price would be the same. Problem 3: Basketballs:

One sporting goods store sells basketballs for $15.00 a ball. The only way to buy stuff from the store is if you have a membership. Membership for the store is free. Their rival sporting goods store sells basketballs for $5.00 a ball with a $20.00 yearly membership.What store would save you more money? So to set up your equation, you would need to bring down the information and make an equation. Let's call it sporting goods store A. They sell the basketballs for $15.00 a ball with a free membership. So that side of the equation will be 15x because the free membership is nothing. Their rival, sporting goods store B, sells basketballs for only $5.00 a ball, but with an additional $20.00 membership. So that side of the equation would be 5x + 20. Now your equation would be:

15x = 5x + 20 Now you need to solve your equation. If you have: 15x = 5x + 20, you can simplify that to something much easier to work with. The trick is to get x on one side of the equation. You want to do what is easier though when you simplify. That would be to subtract 5x. Remember what ever you do to one side, you have to do to the other. It should look like this:

15x = 5x + 20

-5x -5x (subtracting it from both sides!)

You should get:

10x = 20

Now you need to divide by ten to get x alone. It should look like this when you set it up:

10x/(10) = 20/(10)

You should get:

x = 2 All this is saying is that if you want to buy one basketball, you should buy it from sporting goods store A. It will save you more money because if x = 1 15x = 15, but at store B, if x = 1, then 5x + 20 = 25. If you buy two basketballs, the total price would be the same because 15x = 30 and 5x + 20 = 30. If you wanted to buy more than two basketballs, then you should probably buy from sporting goods store B because the additional price for each ball is less then store A. http://www.quia.com/rr/380806.html

ONLINE ACTIVITY ABOVE Vocabulary:

Equation: A statement that the values of two mathematical expressions are equal indicated by an equal sign. --> =

Variable: A symbol for a number we don't know yet.

Coefficient: A number placed before a variable.

Simplify: Getting an equation to its simplest form.

Divide: Splitting into equal parts or groups.

Multiply: The combination of two numbers by multiplication.

Subtract: Taking one number away from another.

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# Common Core State Standards

Solving Equations With Variables On Both Sides

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