Notes on solving equations

1. A QUICK REVIEW
OF ALGEBRA
Jim Smith JCHS

2. Follow These Steps
When Solving Equations
Simplify Both Sides
Get Variables On One Side
Cancel The Add And Subtraction
Cancel The Mult And Division

3. Simplify Both Sides
Of The Equal Sign
( This May Take Several Steps)
Distributive Property
Combine Like Terms
Removing Fractions
2x = 4 (x – 8) + 6x

4. Get Variables On One Side
Of The Equation
If The Equation Has Variables
On Both Sides Of The Equal Sign,
Cancel Out All Variables
On One Side.
3x + 5 = 5x - 7

5. Cancel Any Addition Or
Subtraction With The Variable
Performing The Opposite Operation
With The Same Number Will
Cancel It. Do This To Both Sides.
2x + 7 = 21
7 – 3x = 19

6. Be Neat…. Show Your Work
2x + 5 = 5x - 19
2x + 5 - 2x = 5x - 19 - 2x
5 = 3x - 19
5 + 19 = 3x - 19 + 19
24 = 3x
24 = 3x
3 3
8 = x

7. 5x + 2x = 4 ( x + 3 ) + 6
7x = 4 ( x + 3 ) + 6
7x = 4x + 12 + 6
7x = 4x + 18
7x – 4x = 4x + 18 – 4x
3x = 18
3x = 18
3 3
X = 6

8. 5x – 3
3
= 9
5x – 3
3
= 9
3 3
5x – 3 = 27
5x – 3 +3 = 27 +3
5x = 30
5x = 30
5 5
X = 6
END

10. Given Equation
3(x+2) = x-8
Cup 1

11. Simplify Both Sides
Cup 2
3x+6 = x-8
3(x+2) = x-8

12. Get Variables On One Side
3x+6-x = x-8-x
2x+6 = -8
Cup 3
3x+6 = x-8

13. Cancel The Add or Subtraction
2x+6-6 = -8-6
2x = -14
Cup 4
2x+6 = -8

14. Cancel The Mult And Division
2x = -14
2x = -14
2 2
x = -7
Cup 5

15. 3(x+2) = x-8
3(x+2) = x-8
3x+6 = x-8
3x+6 = x-8
3x+6-x = x-8-x
2x+6 = -8
2x+6 = -8
2x+6-6 = -8-6
2x = -14
2x = -14
2x = -14
2 2
x = -7

16. Given Equation
Simplify Both Sides
Variables On One Side
Cancel Add or Sub
Cancel Mult And Div