1. Multi-Step Equations
We must simplify each expression on the equal sign to look like a one, two, three step equation

2. Steps for solving multi-step equations
If there are fractions, multiply by the LCD to cancel out the denominators
Use the distributive property if necessary
Combine Like terms
Get the variables to one side of the = and the #’s on the other side
Isolate the variable and solve
Check your answer

3. Combing Like Terms
10x – 3 - 4x + 4 = -2x x (10x - 4x) + (-3 + 4) = (-2x + 7x) + 3 6x + 1 = 5x x -5x 1x + 1 = x = 2 or x = 2
Practice: -5x = 18x -8x Answer: X = -26/15

4. Practice
3x – 4x + 8 – 9 = 10
2x – 10 – 8x = 9
4x – 6x – 9x = 33
-4x + 8 – 10 = 12
4x – 3x + 7 = 12x – 6 -9
7 – 3x + 4x = 10
17 x – 10 – 4 = 15x
X = -11
X = 19/-6
X = -3
X = -7/2
X = 2
X = 3
X = -7

5. Distributive Property
-31x + 28 = x = X = 58/31 Practice: 3(x – 5) = x Answer: X = -1
-7(3x – 4) = 10(x -3) Distribute to get ride of the parentheses -21x + 28 = 10x – x -10x -31x + 28 = -30

6. Practice
3(x – 6) = 10
-2(6x – 8) = -8
10 = 3(x + 4)
2(2x – 8) = 4(9 – 5x)
3(x – 8) + 10 = -5x
10 + 6x = -(3x – 9)
4x –(5x – 7) = 20
X = 28/3
X = 2
X = 4/3
X = 52/9
X = 7/4
X = -1/9
X = -13

7. Fractions
6y – 3 = 4
6y = 7 6
Y = 7/6
Practice:
⅖ + ⅙y = -⅔y + ⅓
Answer:
Y = -2/25
¾y - ⅜ = ½ LCD = 8 (8)¾y – (8)⅜ = (8)½ 6y – 3 = 4

8. Solution? Solve the following problem 4x – 8 = 2(-4 + 2x)
When an equation is an identity(true statement) our solution is all real numbers.
Any real number you substitute into the equation will give you a true answer

9. Example: 5(2-x) + 8x = 3(x - 6) When we have an equation with no variables and the statement is not true, our answer is no solution!
There is no real number that will make our equation true