1. Equations with x on both sides
© Victoria Smith
Algebra
Equations with x on both sides
Begin

2. Equations with x on both sides
© Victoria Smith
Equations with x on both sides
10x – 7 = 6x + 5
Next

3. Equations with x on both sides
© Victoria Smith
Equations with x on both sides
10x – 7 = 6x + 5
-6x
First, we want to get all of the x’s on one side of the equation. Remember, if the number we are moving is positive to start with, it becomes negative when we move it over, if it starts as negative, if becomes positive when we move it over.
This gives us:
4x – 7 = 5
Summary
10x – 7 = 6x + 5
4x – 7 = 5
Next

4. Equations with x on both sides
© Victoria Smith
Equations with x on both sides
4x – 7 = 5 +7
Now, we want to get all of the numbers on the other side of the equation. Again remember that if the number we are moving is positive to start with, it becomes negative when we move it over, if it starts as negative, if becomes positive when we move it over.
This gives us:
4x = 12
Summary
10x – 7 = 6x + 5
4x – 7 = 5
4x = 12
Next

5. Equations with x on both sides
© Victoria Smith
Equations with x on both sides
4x = 12
÷ 4
In the last stage, if a number was negative, we did the opposite to it when it moved. The same rule applies when it is multiplied (the opposite is divide).
So on the left side, you are multiplying by 5, this becomes divide by 5 when it moves to the other side.
This gives us:
x = 3
Summary
10x – 7 = 6x + 5
4x – 7 = 5
4x = 12
x = 3
Next

6. Equations with x on both sides
© Victoria Smith
Equations with x on both sides
8x – 3 = 3x + 1
Not every equation will give you an integer (whole number) as a value for x when solved. Let’s work through this one to see what happens:
Next

7. Equations with x on both sides
© Victoria Smith
Equations with x on both sides
8x – 3 = 3x + 1
-3x
First, we want to get all of the x’s on one side of the equation. Remember, if the number we are moving is positive to start with, it becomes negative when we move it over, if it starts as negative, if becomes positive when we move it over.
This gives us:
5x – 3 = 1
Summary
8x – 3 = 3x + 1
5x – 3 = 1
Next

8. Equations with x on both sides
© Victoria Smith
Equations with x on both sides
5x – 3 = 1 +3
Now, we want to get all of the numbers on the other side of the equation. Again remember that if the number we are moving is positive to start with, it becomes negative when we move it over, if it starts as negative, if becomes positive when we move it over.
This gives us:
5x = 4
Summary
8x – 3 = 3x + 1
5x – 3 = 1
5x = 4
Next

9. Equations with x on both sides
© Victoria Smith
Equations with x on both sides
5x = 4
÷ 5
In the last stage, if a number was negative, we did the opposite to it when it moved. The same rule applies when it is multiplied (the opposite is divide).
So on the left side, you are multiplying by 5, this becomes divide by 5 when it moves to the other side.
This gives us:
x = 4/5
Summary
8x – 3 = 3x + 1
5x – 3 = 1
5x = 4
x = 4/5
Next

10. Equations with x on both sides
© Victoria Smith
Equations with x on both sides
7x – 3 = 3x + 8
-3x
First, we want to get all of the x’s on one side of the equation. Remember, if the number we are moving is positive to start with, it becomes negative when we move it over, if it starts as negative, if becomes positive when we move it over.
This gives us:
4x – 3 = 8
Summary
7x – 3 = 3x + 8
4x – 3 = 8
Next

11. Equations with x on both sides
© Victoria Smith
Equations with x on both sides
4x – 3 = 8 +3
Now, we want to get all of the numbers on the other side of the equation. Again remember that if the number we are moving is positive to start with, it becomes negative when we move it over, if it starts as negative, if becomes positive when we move it over.
This gives us:
4x = 11
Summary
7x – 3 = 3x + 8
4x – 3 = 8
4x = 11
Next

12. Equations with x on both sides
© Victoria Smith
Equations with x on both sides
4x = 11
÷ 4
In the last stage, if a number was negative, we did the opposite to it when it moved. The same rule applies when it is multiplied (the opposite is divide).
So on the left side, you are multiplying by 5, this becomes divide by 5 when it moves to the other side.
This gives us:
x = 11/4
Summary
8x – 3 = 3x + 1
5x – 3 = 1
5x = 4
x = 11/4
Next

13. Equations with x on both sides
© Victoria Smith
Equations with x on both sides
You must also remember to give fractions in their lowest or simplest terms, so
x = 11/4
becomes:
x = 2 3/4
Summary
8x – 3 = 3x + 1
5x – 3 = 1
5x = 4
x = 11/4
x = 2 3/4