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INSTRUCTORS Carleen Eaton Grant Fraser Eric Smith
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For more information, please see full course syllabus of Algebra 1
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Lecture Comments (14)

1 answer

Last reply by: Dr Carleen Eaton
Fri Apr 10, 2015 6:26 PM

Post by Craig Goldsmith on April 5, 2015

How would I solve this y=-2x+7

4 answers

Last reply by: Jeremy Canaday
Thu Aug 8, 2013 12:38 PM

Post by Jeremy Canaday on August 4, 2013

For example 3, I am confused due to using the distributive property in the middle of the equation. why would 4 not be used alone in multiplying 14 when separating the variables? Is this due to the unknown variables in the fraction?

1 answer

Last reply by: Jeremy Canaday
Sun Aug 4, 2013 9:49 AM

Post by Jeremy Canaday on August 4, 2013

Dr. Eaton, Would 2n- -4n = 6n? I'm confused by this term simply because in the sentence, 2n is a positive number. I was under the impression that if you turn this statement into a sentence for example you are "taking away" negatives from a positive number. Therefore, if you take away negatives from a positive, are you adding?

1 answer

Last reply by: Dr Carleen Eaton
Tue Feb 19, 2013 7:51 PM

Post by bo young lee on February 13, 2013

if i after sloving a equation there a final equation i dont know how to find the no solution or infinte solution
ex:3x+4=3x+4 or 3f+7=6+2f

2 answers

Last reply by: bo young lee
Wed Feb 13, 2013 9:13 PM

Post by bo young lee on February 7, 2013

i keep wonder how to find the no solution and infinte solution.

When the Variable is on Both Sides of the Equation

  • A more complicated equation in one variable could have grouping symbols and the variable on both sides. To solve such an equation: first eliminate grouping symbols by using the distributive property and applying a negative sign preceding a grouping symbol to each term inside the group. Then, if the resulting equation has the variable on both sides, use the addition or subtraction properties of equality to eliminate the variable from one side of the equation or the other and to get all the constants on the other side. Finally, solve this simplified equation using the multiplication or division property.
  • Some equations are true for all values of the variable. These are called identities.
  • Other equations are not true for any values of the variable.

When the Variable is on Both Sides of the Equation

3n − 6 = 5n + 9
  • 3n − 6 − 5n = 5n + 9 − 5n
  • − 2n − 6 = 9
  • − 2n − 6 + 6 = 9 + 6
  • − 2n = 15
  • [( − 2n)/( − 2)] = [15/( − 2)]
n = − 7.5
5x + 8 = 13x − 9
  • 5x + 8 − 13x = 13x − 9 − 13x
  • − 8x + 8 = − 9
  • − 8x + 8 − 8 = − 9 − 8
  • − 8x = − 17
x = [17/8]
7( 3x + 5 ) = 2( 12x − 8 ) + 14
  • 21x + 35 = 24x − 16 + 14
  • 21x + 35 = 24x − 2
  • 21x + 35 − 24x = 24x − 2 − 24x
  • − 3x + 35 = − 2
  • − 3x + 35 − 35 = − 2 − 35
  • − 3x = − 37
x = [37/3]
2( 13x − 5 ) = 2 − ( 6 − 5x )
  • 26x − 10 = 2 − 6 + 5x
  • 26x − 10 = − 4 + 5x
  • 26x − 10 − 5x = − 4 + 5x − 5x
  • 21x − 10 = − 4
  • 21x − 10 + 10 = − 4 + 10
  • 21x = 14
  • x = [14/21] = [2/3]
x = [2/3]
2( 8y + 11 ) / 4 = 6( y − 5 )
  • 16y + 22 / 4 = 6y − 30
  • 4( [(16y + 22)/4] ) = ( 6y − 30 )4
  • 16y + 22 = 24y − 120
  • 16y + 22 − 24y = 24y − 120 − 24y
  • − 8y + 22 = − 120
  • − 8y + 22 − 22 = − 120 − 22
  • − 8y = − 142
  • y = [142/8] = [71/4]
y = [71/4]
4( 6s + 2 ) = 8( 3 − 2s )
  • 24s + 8 = 24 − 16s
  • 24s + 8 + 16s = 24 − 16s + 16s
  • 40s + 8 = 24
  • 40s + 8 − 8 = 24 − 8
  • 40s = 16
  • s = [16/40] = [2/5]
s = [2/5]
8n − 14 = 5n − 20
  • 8n − 14 − 5n = 5n − 20 − 5n
  • 3n − 14 = − 20
  • 3n − 14 + 14 = − 20 + 14
  • 3n = − 6
n = − 2
3(5f − 6) = 2(12f − 4) + 13
  • 15f − 18 = 24f − 8 + 13
  • 15f − 18 = 24f + 5
  • 15f − 18 − 24f = 24f + 5 − 24f
  • − 9f − 18 = 5
  • − 9f − 18 + 18 = 5 + 18
  • − 9f = 23
  • [( − 9f)/( − 9)] = [23/( − 9)]
f = − [23/9]
[(5(4x − 8))/10] = 2(15x + 5)
  • [(20x − 40)/10] = 30x + 10
  • 10( [(20x − 40)/10] ) = (30x + 10)10
  • 20x − 40 = 300x + 100
  • 20x − 40 − 300x = 300x + 100 − 300x
  • − 280x − 40 = 100
  • − 280x − 40 + 40 = 100 + 40
  • − 280x = 140
  • x = − [140/280] = − [1/2]
x = − [1/2]
4(4k − 8) = 4(3k − 6) − 18 − 2k
  • 16k − 32 = 12k − 24 − 18 − 2k
  • 16k − 32 = 10k − 42
  • 16k − 32 − 10k = 10k − 42 − 10k
  • 6k − 32 = − 42
  • 6k − 32 + 32 = − 42 + 32
  • 6k = − 10
  • k = − [10/6]
k = − [5/3]

*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

When the Variable is on Both Sides of the Equation

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
  • Solving More Complicated Equations 0:28
    • Distributive Property
    • Review of Distributive Property
    • Factoring
    • Subtracting
    • Applying with Addition/Subtraction
  • Possible Outcomes 2:45
    • Exactly One Solution
    • No Solution
    • True for All Real Numbers
    • Identities
  • Example 1: Solve Equation 6:03
  • Example 2: Solve Equation 9:08
  • Example 3: Solve Equation 14:06
  • Example 4: Solve Equation 17:28