For more information, please see full course syllabus of Pre Algebra

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For more information, please see full course syllabus of Pre Algebra

For more information, please see full course syllabus of Pre Algebra

### Solving Multi-Step Equations

- Use the Distributive Property, if necessary, collect like terms, and simplify to simplify Multi-Step Equations. At every step in the process of solving an equation, the new equation must be equivalent.
- You can save time and work if you first examine the equation for terms that can be combined or simplified before using any further steps to isolate the variable.
- You can always check your work by substituting you solution to see if the equation is true.

### Solving Multi-Step Equations

9x + 5 − 2x = 8. Solve for x.

- 9x − 2x = 8 − 5
- 7x = 3

x = [3/7]

− 35 = 7x − 12 − 5x. Solve for x.

- − 35 + 12 = 7x − 5x
- − 23 = 2x

x = − [23/2]

For Christmas, a classroom is collecting canned food for the nearby homeless shelter. The class goal is to collect 100 cans of food. The 25 students in the class bring 2 cans each. How many more cans does each student need to bring to meet the class goal?

- 100 = 25(2 + c), where c = number of cans each student still has to bring
- 100 = 50 + 25c
- 50 = 25c

c = 2 cans

Your family and friends go to see a movie together. A student ticket costs $ 8 and an adult ticket costs $ 12. There are 5 female students and 2 adults. If the total cost of the tickets was $ 96, how many male students went to see the movie?

- Let a = number of adults, f = number of female students, and m = number of male students.
- $ 8(f + m) + $ 12a = $ 96
- $ 8(5 + m) + $ 12(2) = $ 96
- $ 40 + $ 8m + $ 24 = $ 96
- $ 64 + $ 8m = $ 96
- 4$ 8m = $ 32

m = 4 male students

4a + 10 − a + 7 = 23. Solve for a.

- 3a + 17 = 23
- 3a = 6

a = 2

− 3(x + 7) = − 36. Solve for x.

- − 3x − 12 = − 36
- − 3x = − 24

x = 8

2([3/2]x + 5) − 7x = − 10. Solve for x.

- 3x + 10 − 7x = − 10
- − 4x = − 10

x = [5/2]

7x(3) − 7 − 3x = − 5. Solve for x.

- 21x − 7 − 3x = − 5
- 18x = 2

x = [1/9]

− 64 = 8x + 24 − 11x + 8. Solve for x.

- − 64 = − 3x + 32
- − 96 = − 3x

x = 32

1.2x + 3.6 − 3.2x = 8. Solve for x.

- − 2x = 4.4

x = − 2.2

*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

### Solving Multi-Step 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 You'll Learn and Why 0:06
- Topics Overview
- Vocabulary 0:17
- Like Terms
- Distributive Property
- Simplifying Before Solving an Equation 1:37
- Example: 8x + 45 - 12x = 9
- Example: -15 = 6b + 12 - 3b + 6
- Using the Distributive Property 4:50
- Example: Haiti Relief Efforts
- Using the Distributive Property 7:50
- Example: Amusement Park
- Extra Example 1: Simplify and Solve 11:34
- Extra Example 2: Simplify and Solve 12:21
- Extra Example 3: Simplify and Solve 13:18
- Extra Example 4: Mailing Letters 14:53

1 answer

Last reply by: Professor Fung

Sat Sep 29, 2012 7:37 AM

Post by Michael Trow on September 26, 2012

Extra Example IV she does not make any sense the minus t( -t) she says is there not to be charged twice but if it as it is stated the first ounce is 0.39 and additional ounces 0.24 why are we subtracting the 0.24 from the minus 0.39 which is essentially what this minus t does thus making the first ounce arbitrary. Not logical no sound explanation, if someone else can explain it better that would be great

0 answers

Post by NARASIMHARAO GOTTIPATI on August 16, 2012

the right answer for -15=3b+12+6 is b= -11

0 answers

Post by julius mogyorossy on August 9, 2011

In the future Professors will only be there to answer questions you have because you were too stupid to understand the videos. Plus, to grade your tests, or maybe they will have robots grade your tests. I am creating ASCII mathematical, terms, ie, 10'-10=ten to the negative tenth power, it works for me, easier to make notes, I need something for the the cube square root of 27, any ideas. Obviously I don't have a math editor.

0 answers

Post by julius mogyorossy on August 9, 2011

I may be stupid, I may be insane, as so maybe would believe, but I know how much 15-16=, I love Nancy, but she does seemed burned out, I don't blame her, that is why these math videos are so awesome, they are the future of education. Dr. Rish, I am so grateful to you for bringing me Educator.com. Thanks.

0 answers

Post by julius mogyorossy on August 9, 2011

When trying to solve multi step equations I would imagine a higher level of abstraction, a God number if you will, standing above the expression, looking down in contempt, it seems to work for me, I shall let you know if I learn differently.

2 answers

Last reply by: julius mogyorossy

Tue Aug 9, 2011 4:35 PM

Post by Alexey Shevelyov on April 30, 2011

- 15 + - 18 = -33

Mistakes are in every other lesson guys!

Please pay your attention!