Solving linear equations using distributive property: a(x + b) = c

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Intros
Lessons
    • What is Distributive Property?
    • How to use distributive property to solve linear equations?
  1. How to turn a word problem into an equation?
    • ex. 1: "revenue" problem
    • ex. 2: "area" problem
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Examples
Lessons
  1. Solve.
    1. 11.32=8(0.61+x)11.32 = 8\left( {0.61 + x} \right)
    2. 5(2.49+x)=17.46 - 5\left( {2.49 + x} \right) = 17.46
    3. 2(x18.5)=4.672\left( {x - 18.5} \right) = - 4.67
    4. 9.5=11.5(x5.2)9.5 = - 11.5\left( {x - 5.2} \right)
  2. Find the value of xx.
    1. 3.57+x2=2.16\frac{{3.57 + x}}{2} = 2.16
    2. 6.79=x3.434 - 6.79 = \frac{{x - 3.43}}{4}
    3. 0.761=0.158+x2 - 0.761 = \frac{{0.158 + x}}{{ - 2}}
    4. x20.915=8.25\frac{{x - 20.91}}{{ - 5}} = 8.25
  3. A grocery store has chocolate bars on sale. Each chocolate bar is $0.25 cheaper when 4 of them are purchased. Chris bought 4 chocolate bars, and he paid $8.52. What is the original price of each chocolate bar?
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    Practice
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    Topic Notes
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    When you see equations in the form of a(x+b) =c, you can remove the bracket and rewrite the equations into ax+ab =c using the distributive property. In this lesson, we will make use of this property to help us solve linear equations.

    What is distributive property?

    What is the definition of distributive property? Sometimes called the distributive law of multiplication and division, distributive property helps us solve equations like a(b+c). In distributive property, you'll have to take the numbers from inside the parentheses out (factor them out) by multiplying what's outside with the terms inside.

     

    How to do distributive property

    In order to tackle the distributive property, first recognize the question you're given and whether distributive property is the appropriate method to use.

     

    Let's take a(b+c). In this case, if b+c can no longer be simplified (remember you're supposed to solve everything inside parentheses first), then you'll take "a" and multiply it with the two different terms inside the parentheses, which consists of "+b" and "+c". Take note of the signs in front of the terms. Multiplying in "a" with these two terms gives us:

    a(b+c) = ab+ac

    If it was a(b-c), we'll be multiplying a with the terms "+b" and "-c". This will give us:

    a(b-c)=ab-ac

    Be mindful of the sign so that you don't end up with the wrong answer. Here's a reference to a color coded explanation of the distributive property if you need to visualize the concept.

     

    example of distributive property

    Let's try solving equations using distributive property. We'll guide you through two ways that the following question can be solved.

     

    Question: 11.32 = 8(0.61 + x)

     

    Solution1:

     

    1. 11.32 = 8(0.61+x)
    2. Divide both side by 8, you get  1.415 = 0.61 +x
    3. Minus both side by 0.61, 0.805 = x

     

    In this solution, we first try to move all the non-x terms over to one side. The first step of dividing both sides by 8 helps us move the 8 from the right side to the left side. This allows us to get rid of the parentheses too as the terms no longer have to be multiplied out (there's nothing to multiply them with). Then, in order to move 0.61 to the left side, we'll minus it from both sides. In the end, we'll get that x ultimately equals 0.805.

     

    Solution 2:

     

    1. 11.32 = 8(0.61+x)
    2. Open up the right side, you get 11.32 = 4.88+8x
    3. Minus both side by 4.88, you get  6.44 = 8x
    1. Divide both side by 8, you get  0.805 = x

     

    In solution 2, we're truly using the distributive property. We're going to distribute 8 into the terms in the parentheses, which are "+0.61" and "+x". This gives us 4.88 + 8x on the right side of the equation. Then we can move over 4.88 to the left side with the rest of the non-x terms by minusing it from both sides. Lastly, divide both sides by 8 to move the 8 over to the left side and you'll find that x = 0.805. Both methods will bring you to the same correct answer.

     

    Try out more distributive property examples on StudyPug that can help you firmly grasp the concept before your next test. If you want more questions, feel free to look online for a distributive property worksheet and apply the same method we've shown you to solve the problems.