Solve Multi-step Solve Multi-step EquationsEquations

Students will solve equations with multiple steps (more than two) using distributive property, combining like

terms, and inverse operations.

POWER to the brain.

3 ( x – 4 ) =

64x + 7 ( x – 2 ) = -8

m – 9 – ( 3m + 4 ) = 1

-3 = 3a + 5 ( a – 9 ) + 4

REVIEW: Simplify Using the Distributive Property.

Distributive Property – Multiply times everything in the parentheses.

a ( b + c ) = ab + ac

Example 1: -3 ( x + 5 )

-3x – 15

Example 2: -7 ( 2a – 4 )

-14a + 28

OR a ( b – c ) = ab – ac

REVIEW: Simplify Using Combining Like Terms

Like Terms must have the same variables and the same powers on the letters.

Combine like terms by adding or subtracting the coefficients (numbers in front of the variables).

Example 1: 3x + 5 – 7x + 9

-4x + 14Example 2: 3 – 6y – 7 – 9y

-4 – 15y

How do we simplify and solve How do we simplify and solve equations with multiple steps?equations with multiple steps?

To solve equations with multiple steps, first use the distributive property to get

rid of the parentheses.

Then, combine like terms to get the problem in the 2-step form.

Solve by using inverse operations as you do with 2-step equations.

Simplify and Solve

Example: 3x + 2 ( 2x – 1 ) = 33

4x – 2 3x + = 33

7x – 2 = 33

+ 2 + 2

7x = 35

7 7

x = 5

1.Use Distributive Property

2. Combine Like terms

3. Use Inverse Operations

Simplify and Solve Equations

Example: 3 ( x – 2 ) + 4x = 8FIRST - Use the

Distributive Property to get rid of the parentheses.3x – 6 + 4x = 8

Copy the rest of the problem.

SECOND: Combine like

terms.7x – 6 = 8

+ 6 + 6

7x = 14 Divide both sides by 7.7 7

x = 2

Add 6 to both sides.Now it’s a regular 2-step

equation.

Use your calculator for the computations if

needed.

Simplify and SOLVE: -4y – 5 – 4( -2y – 3 ) + 8 = 3

+ 8y + 12- 4y – 5 + 8 = 3

4y + 7 + 8 = 3

+ 15 = 34y

Distributive Property

Copy the rest of the problem.

Combine like terms.

– 15 – 15

4y = -124 4y = -3

Use your calculator for the computations if

needed.

Simplify and Solve:-5x + 3 – ( 9x – 2 ) + 7 = 96

– 9x + 2-5x + 3 + 7 = 96

Distributive Property

Combine Like Terms

-14x + 12 = 96– 12 – 12

-14x = 84-14 -14

x = - 6

Use your calculator for the computations if

needed.

SUMMARYSUMMARYTo solve equations with multiple steps, first use the distributive property to get

rid of the parentheses.

Then, combine like terms to get the problem in the 2-step form.

Solve by using inverse operations as you do with 2-step equations.

1. 2n + 3n + 7 = -41 2. 2x - 5x + 6.3 = -14.4 3. 2z + 9.75 - 7z = -5.154. 3h - 5h + 11 = 17 5. 2t + 8 - t = -3 6. 6a - 2a = -367. 3c - 8c + 7 = -18 8. 7g + 14 - 5g = -8 9. 2b - 6 + 3b = 1410. 2(a - 4) + 15 = 13 11. 7 + 2(a - 3) = -9 12. 13 + 2(5c - 2) = 2913. 5(3x + 12) = -15 14. 4(2a + 2) - 17 = 15 15. 2(m + 1) = 16

16. -4x + 3(2x - 5) = 31 17. -6 - 3(2k + 4) = 18 18. 3(t - 12) = 2719. -w + 4(w + 3) = -12 20. 4 = 0.4(3d - 5) 21. -4d + 2(3 + d) = -1422. 2x + (4x + 16) = 7 23. 2(3a + 2) = -8 24. 5(t - 3) - 2t = -3025. 5(b + 4) - 6b = -24 26. (5k + 35) - 8 = 12 27. 0.4(2s + 4) = 4.828. (9b - 27) = 36 29. (12n - 8) = 26 30. 0.5(2x - 4) = -17

Copy the problems and solve for the variable. Be sure you show all your steps to receive full credit. NO WORK = NO CREDIT

Practice: Multi-step Equations 1Practice: Multi-step Equations 1

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