1. Solving EQUATIONS Lesson #2 created by: ms. Guarnieri

2. ONE STEP EQUATIONS
An equation is like a balance scale because it shows that two quantities are equal.
What you do to one side of the equation must also be done to the other side to keep it balanced.
REMEMBER – START WITH ADDITION
AND SUBTRACTION AND DO THE OPPOSITE!!!!

3. Solving an addition equation: t + 7 = 21
Example 1
Solving an addition equation:
t + 7 = 21
Get rid of the 7 by adding its opposite to both sides of the equation. -7 -7
t = 14
Created by S. Koch

4. Solving a subtraction equation: g – 6 = 40
Example 2
Solving a subtraction equation:
g – 6 = 40
Get rid of the 6 by adding its opposite to both sides of the equation. +6 +6
g = 46
Created by S. Koch

5. Solving a multiplication equation: 8n = 32
Example 3
Solving a multiplication equation:
8n = 32
Get rid of the 8 by dividing both sides of the equation by 8. Here we “undo” multiplication by doing the opposite – division.
8n = 32 8 8
n = 4
Created by S. Koch

6. Solving a division equation: k / 9 = 11
Example 4
Solving a division equation:
k / 9 = 11
Get rid of the 9 by multiplying both sides of the equation by 9. Here we “undo” division by doing the opposite – multiplication.
x 9
x 9
k = 99
Created by S. Koch

7. Practice Problems
Please take a few moments to complete the following practice problems in your notes.
2x = 18
10x = 70
x/2 = 100
-x/5 = 12
4x = 20

8. What??? I just learned 1-step!
Relax. You’ll use what you already know to solve 2-step equations.

9. + - STEP 1 The first step will always be either adding or
subtracting. DO THE OPPOSITE, whatever you do to one side, do to the other. + -

10. ÷ • STEP 2 The second step will always be either
multiplying or dividing. DO THE OPPOSITE, whatever you do to one side, do to the other. ÷ •

11. 8x + 5 = 61 - 5 - 5 = 56 8x Let’s try a problem.
This problem has addition, so we need to subtract first.
Whatever we do on one side, we have to do on the other. = 56 8x

12. Now, Step 2.
8x = 56
Whatever we do on one side, we have to do on the other.
This problem has multiplication, so we need to divide now. 8 8 x 7 =

13. Let’s try another problem.
+ 8
+ 8
This problem has subtraction, so we need to add first.
Whatever we do on one side, we have to do on the other. = 12 3a

14. Now, Step 2.
3a = 12
Whatever we do on one side, we have to do on the other.
This problem has multiplication, so we need to divide now. 3 3 a 4 =

15. Now you try some problems.
Copy these problems onto a piece of paper.
Break each problem into 2 parts to solve.
Show all your work!
12t – 6 = 90
7f + 5 = 40
5q – 7 = 13
4y + 8 = -12

16. Solving Equations with
Variables on both sides

17. 1) Solve. 3x + 2 = 4x - 1
You need to get the variables on one side of the equation. It does not matter which variable you move. Try to move the one that will keep your variable positive.

18. 1) Solve 3x + 2 = 4x - 1 - 3x - 3x 2 = x - 1 + 1 + 1 3 = x
3 = x
3(3) + 2 = 4(3) - 1
9 + 2 =
Draw “the river”
Subtract 3x from both sides
Simplify
Add 1 to both sides
Check your answer

19. 2) Solve 8y - 9 = -3y + 2 + 3y + 3y 11y – 9 = 2 + 9 + 9 11y = 11 11 11
11y =
y = 1
8(1) - 9 = -3(1) + 2
Draw “the river”
Add 3y to both sides
Simplify
Add 9 to both sides
Divide both sides by 11
Check your answer

20. 3) Solve 4 = 7x - 3x 4 = 4x 4 4 1 = x 4 = 7(1) - 3(1) Draw “the river”
1 = x
4 = 7(1) - 3(1)
Draw “the river”
– Notice the variables are on the same side!
Combine like terms
Divide both sides by 4
Simplify
Check your answer