Multi-Step Equations

We must simplify each expression on the equal sign to look like a one, two,

three step equation

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

Combing Like Terms

10x – 3 - 4x + 4 = -2x + 3 + 7x

(10x - 4x) + (-3 + 4) = (-2x + 7x) + 3

6x + 1 = 5x + 3-5x -5x

1x + 1 = 3 -1 -11x = 2 or x = 2

Practice:

-5x -7 -19 = 18x -8x

Answer:

X = -26/15

• 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

Distributive Property

-7(3x – 4) = 10(x -3)

Distribute to get ride of the parentheses

-21x + 28 = 10x – 30-10x -10x -31x + 28 = -30

-31x + 28 = -30 -28 -28

-31x = -58-31 -31

X = 58/31

Practice: 3(x – 5) = -10 + 8xAnswer:X = -1

• 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

Fractions

¾y - ⅜ = ½

LCD = 8

(8)¾y – (8)⅜ = (8)½

6y – 3 = 4

6y – 3 = 4 +3 +3

6y = 76 6

Y = 7/6

Practice:⅖ + ⅙y = -⅔y + ⅓Answer: Y = -2/25

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

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