Solving Equations with Variables

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Solving Equations with Variables

• Created by Cheri Sandford
• Liberty Middle School, 2005

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Wait a minute! Whats a variable?

• A variable is a letter in an equation. It can
  mean any number.

A variable does not have to stand for the same
number in every equation. It can be different
every time.
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So, how am I supposed to figure out a math
problem without all the numbers?

• When we solve equations with variables, we move
  parts of the equation around until we get the
  variable (the letter) by itself. Then we will
  find out what number the variable means.

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Lets try one.

• 8 y 11

We need to get the variable y by itself. So we
will need to get rid of the 8 by subtracting it.
8 y 11
If we subtract 8 from one side of the equation,
we have to subtract 8 from the other side.
- 8
- 8
y
0

3
5
Lets check that answer to see if it is correct.

• 8 y 11

We need to put in our answer (3) where the
variable (y) is to see if it makes sense.
8 3 11
8 3 does equal 11, so our answer makes sense.
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Lets look at another problem..

• z - 5 4

We need to get the variable z by itself. So we
will need to get rid of the -5 by adding its
opposite, 5.
z - 5 4
If we add 5 to one side of the equation,
we have to add 5 to the other side.
5
5
z
9
- 0

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Lets check that answer to see if it is correct.

• z - 5 4

We need to put in our answer (9) where the
variable (z) is to see if it makes sense.
9 - 5 4
9 - 5 does equal 4, so our answer makes sense.
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Copy down these equations in your notebook and
solve them.

• 7 x 21
• c 2 98
• b 9 13
• g 8 20
• 11 p 50