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## Discussion

## Study Guides

## Practice Questions

## Download Lecture Slides

## Table of Contents

## Related Books

### Techniques for Multistep Equations

- A multi-step equation contains more than one operation.
- To solve such an equation, undo the operations in the reverse order in which they were performed in the equation. The last operation performed in the equation is the first one to be removed, using the addition, subtraction, multiplication, and division properties of equality.
- In most equations, the last operation performed is an addition or subtraction. Therefore, begin by using these properties of equality. Then use the multiplication or division property of equality to isolate the variable.
- Understand how to solve word problems involving consecutive numbers. Consecutive unknown numbers are called x and x + 1. Consecutive unknown even or odd numbers are called x and x + 2.

### Techniques for Multistep Equations

3y - 11 = 37

- 3y - 11 + 11 = 37 + 11
- 3y = 48

y = 16

89 = 17 - 6x

- 89 - 17 = 17 - 6x - 17
- 72 = - 6x
- 12 = - x

- 12 = x

[(a − 7)/4] = 11

- 4( [(a − 7)/4] ) = 11(4)
- a - 7 = 44
- a - 7 + 7 = 44 + 7

a = 51

16 = [(45 − t)/3]

- 3(16) = ( [(45 − t)/3] )3
- 48 = 45 - t
- 48 - 45 = 45 - t - 45
- 3 = - t

- 3 = t

9 = [(17 + b)/5]

- 5(9) = ( [(17 + b)/5] )5
- 45 = 17 + b
- 45 - 17 = 17 + b - 17

28 = b

Three consecutive numbers have a sum of fifty - four. Find the numbers.

- x, x + 1 ,x + 2 represent the three consecutive numbers
- x + (x + 1) + (x + 2) = 54
- 3x + 3 = 54
- 3x + 3 - 3 = 54 - 3
- 3x = 51

x = 17

Five consecutive numbers have a sum of one hundred. Find the numbers.

- x, x + 1, x + 2, x + 3, x + 4 represent the five consecutive numbers.
- x + (x + 1) + (x + 2) + (x + 3) + (x + 4)
- 5x + 10 = 100
- 5x + 10 - 10 = 100 - 10
- 5x = 90

x = 18

[(3m + 10)/4] + 6 = 18

- [(3m + 10)/4] + 6 − 6 = 18 − 6
- [(3m + 10)/4] = 12
- 4( [(3m + 10)/4] ) = 12(4)
- 3m + 10 = 48
- 3m + 10 - 10 = 48 - 10
- 3m = 38

m = [38/3]

− 8 = [(5 − c)/2] + 10

- − 8 − 10 = [(5 − c)/2] + 10 − 10
- − 18 = [(5 − c)/2]
- 2( − 18) = ( [(5 − c)/2] )2
- - 36 = 5 - c
- - 36 - 5 = 5 - c - 5
- - 41 = - c

41 = c

[(6y − 3)/10] − 12 = 36

- [(6y − 3)/10] − 12 + 12 = 36 + 12
- [(6y − 3)/10] = 48
- 10( [(6y − 3)/10] ) = 48(10)
- 6y - 3 = 480
- 6y - 3 + 3 = 480 + 3
- 6y = 483

y = 80.5

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

Answer

### Techniques for Multistep Equations

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

- Intro 0:00
- What are Multistep Equations 0:06
- Addition/Subtraction and Multiplication/Division
- Strategy 0:43
- Identify Last Operation
- Example 1: Solve Equation 1:51
- Example 2: Solve Equation 5:27
- Example 3: Find Numbers 7:39
- Example 4: Solve Equation 11:27

1 answer

Last reply by: Dr Carleen Eaton

Sat Jul 27, 2013 9:44 AM

Post by Yolanda Britt on July 5, 2013

what about really long equations

1 answer

Last reply by: Dr Carleen Eaton

Wed Jun 26, 2013 11:28 PM

Post by Taylor Wright on June 17, 2013

In example 2:

Couldn't it be written as (z/5)-(14/5) ? In this case, how would someone know that the division wasn't performed first?

ie: (10/5)-(15/5) equals both 2-3 which = -1 and (10-15)/5 which = -1

It seems that either order the problem is performed in this instance, that the result remains the same, so how would one know which order for the example 2? Could you also add (14/5) to both sides and get the same result?

1 answer

Last reply by: Dr Carleen Eaton

Sun Oct 21, 2012 7:40 PM

Post by Jona James on October 12, 2012

on example 2 i know to get rid of the division you multiply 5 on both sides, and the ''5'' on the left side cancels out, while doing the math on the opposite side, but why?? why does the 5 on the left side cancel out? i memorize the rule but frustrating not knowing why, i think i know the answer i just forgot,,, thank you

1 answer

Last reply by: Dr Carleen Eaton

Thu Aug 9, 2012 5:59 PM

Post by Nagayasu Toshitatsu on August 9, 2012

For example III, I think it would be easier if you set x as the middle number. Then, you would have (x-1)+(x)+(x+1)=66. You can take out the parentheses, and cancel out the ones. After that, you would get 3x=66, which immediately leads to the answer that x=22, and finding out the consecutive numbers. I think it would be easier that way.

1 answer

Last reply by: Dr Carleen Eaton

Wed May 12, 2010 12:06 AM

Post by shah Mahmoodi on April 17, 2010

Excellent, excellent I love it thank you so much Dr Carleen you me bless with your knowledge; I also found your video us full