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### Addition and Subtraction Techniques

- Solving an equation means finding all values of the variable that make the equation true.
- To solve an equation, isolate the variable on one side of the equation and with a coefficient of 1.
- You can do this by using the addition and subtraction properties of equality: If you add or subtract the same quantity to both sides of an equation, the resulting equation has the same solutions as the original equation.

### Addition and Subtraction Techniques

40 + x = - 22

- 40 + x - 40 = - 22 - 40

x = - 64

10 = 54 - y

- 10 - 54 = 54 - y - 54
- - 44 = - y

44 = y

r − [1/5] = [2/5]

- r − [1/5] + [1/5] = [2/5] + [1/5]

r = [3/5]

[5/8] = [2/8] − t

- [5/8] − [2/8] = [2/8] − t − [2/8]
- [3/8] = − t

− [3/8] = t

Thirty - five is six more than a number. Find the number.

x = unknown number

x = unknown number

- 35 = 6 + x
- 35 - 6 = 6 + x - 6

29 = x

Twelve less than a number is sixty six. Find the number.

n = unknown number

n = unknown number

- n - 12 = 66
- n - 12 + 12 = 66 + 12

n = 78

Eighteen is thirty - two less than a number. Find the number.

n = unknown number

n = unknown number

- 18 = n - 32
- 18 + 32 = n - 32 + 32

50 = n

The sum of 6, 8, and a number is equal to 30. What is the number?

x = unknown number

x = unknown number

- 6 + 8 + x = 30
- 14 + x = 30
- 14 + x - 14 = 30 - 14

x = 16

The difference of 55 and a number is equal to 23. What is the number?

x = unknown number

x = unknown number

- 55 - x = 23
- 55 - x - 55 = 23 - 55
- - x = - 32

x = 32

The sum of 21.8, 60.1 and a number is equal to 111.5. What is the number?

x = unknown number

x = unknown number

- 21.8 + 60.1 + x = 111.5
- 81.9 + x = 111.5
- 81.9 + x - 81.9 = 111.5 - 81.9

x = 29.6

*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

### Addition and Subtraction Techniques

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
- Techniques 0:21
- Addition Principle
- Example
- Subtraction Principle
- Example
- Strategy 2:33
- Isolate the Variable
- Example
- Example 1: Solve Equation 3:39
- Example 2: Solve Equation 5:38
- Example 3: Word Problem 7:38
- Example 4: Word Problem 11:14

1 answer

Last reply by: Dr Carleen Eaton

Sat Dec 6, 2014 8:04 PM

Post by patrick guerin on November 28, 2014

On question 1 (40+x=-22),the answer that was there was -64. According to my calculations, there isn't any way that -64 could be the answer. Am I doing some wrong, or was there a slight error in the practice question?

1 answer

Last reply by: Dr Carleen Eaton

Sat Aug 3, 2013 4:12 PM

Post by Jeremy Canaday on August 3, 2013

Dr. Eaton, if I just use simple logic in solving these problems, do you think it would hinder my further learning in algebra 1? As I watch you do these problems, I see at least 2 other ways of answering.

2 answers

Last reply by: Karl Mcculloch

Sun Jun 9, 2013 9:14 AM

Post by Karl Mcculloch on June 5, 2013

on example 4 when simplifying 2 3/4 and 42 2/3 in into decimal form how did you round it to 2.75 and 42.67

1 answer

Last reply by: Dr Carleen Eaton

Sat Aug 25, 2012 12:46 PM

Post by liz lozano on August 21, 2012

how did you get 42.67 on exaple 4 im lost