Download Section 2-13

Chapter 2-13
Name_______________Homeroom______
Solving Equations
An equation is a mathematical sentence that uses an equal sign to show that
two expressions are equal. An equation can either be true or false:
4 + 6 = 10 is true.
5 – 2 = 4 is false.
2(15) = 30 is true.
9 = 5 is false.
*Parentheses mean multiply.
3
An equation is like a scale with the equal sign in the middle:
2+x
=
5
Both sides have the same value. They must always stay in balance.
When we solve an equation, we are finding the value of x. To find x we use
the opposite or “inverse” operation:

Addition and Subtraction are opposite or inverse operations.

Multiplication and Division are opposite or inverse operations.
To solve for 2 + x = 5, you must get x by itself on one side. (Therefore, subtract
2 from both sides.) *If you do the same thing to both sides of the equal sign, the equation will stay in balance.
2+x=5
In this equation, the operation is addition.
-2
-2 Get x by itself (opposite or inverse operation)
0 + x = 3 So x = 3 is the solution or answer.
Checking your answer: Use the original equation to substitute the answer in
place of the variable and then solve. ( 2 + 3 = 5 )
Now you try some! Don’t forget to use the inverse operation. Look back for
help.
10 + y = 14
r + 22 = 30
t–6=3
w – 15 = 40
Check your answers below:
10 + _ = 14
_ + 22 = 30
_-6=3
_ - 15 = 40
To solve for 3x = 15, you must get x by itself on one side. (Therefore, divide
both sides by 3.) *If you do the same thing to both sides of the equal sign, the equation will stay in balance.
3x = 15
In this equation, the operation is
multiplication.
3x = 15
3
3
Get x by itself (opposite or inverse operation).
1x = 5
So x = 5 is the solution or answer.
Checking your answer: Use the original equation to substitute the answer in
place of the variable and then solve. 3(5) = 15
Now you try some! Don’t forget to use the inverse operation. Look back for
help.
6z = 48
8k = 72
Check your answers below:
6( _ ) = 48
8( _ ) = 72
m =4
5
_ =4
5
s =7
11
_ =7
11
Sometimes it takes more steps to get the solution. When the variable is the divisor (the one
you “divide by”), you must take one extra step to solve for the variable.
20 = 4
x
20x = 4x
x
20 = 4x
20 = 4x
4
4
5 =x
In this equation, the operation is division, but the variable is now the divisor.
Use the inverse operation. Remember you must do the same things on both
sides of the equal sign.
(x  x=1)
You can take it from here… Use the inverse operation and solve.
Get x by itself (opposite or inverse operation).
So x = 5 is the solution or answer
Checking your answer: Use the original equation to substitute the answer in
place of the variable and then solve. 20 = 4
5
Now you try some! Don’t forget to use the inverse operation. Look back for
help.
32 = 8
z
Check your answers below:
32 = 8
_
27 = 3
y
27 = 3
_