Lesson 9 — Activity 2: Two-Step Equations



Getting Ready


In the previous activity, you learned about solving one-step equations. Next, you will learn how to use the two-step method.


Try This:

Answer the following question using the one-step method :

d + 25 = 75


d + 25 – 25 = 75 – 25

d = 50


For this lesson, you will learn about the two-step method for answering algebraic questions. A two-step equation is as straightforward as it sounds. You will need to perform two steps in order to solve the equation.

For example, let's use the equation 2x + 4 = 6.


Remember, your goal is always to get the variable by itself. The steps in the two-step method are the same as in the one-step method that you just learned about. The only difference, is that you have to perform two steps in order to get the variable by itself.


Follow these steps:


1. Subtract 4 from both sides.

          2x + 4 – 4 = 6 – 4

          2x = 2


2. Next, you need to divide both sides by 2 to get the variable by itself.

          2x = 2
           2  =  2  

           x = 1


Another example would be 3g – 19 = 8.

In this case, Step 1 would be to add 19 to both sides as follows:

3g – 19 + 19 = 8 + 19

3g = 27


Step 2 is to divide both sides by 3 to get g by itself.

 3g  = 27

  3        3

   g = 9


But what if we have a variable divided by a number in the question? We can still use the two-step approach to get an answer.

For example, if we are given the following equation:

 b  + 7 = 9

 2

we can solve it this way:

Step 1:

Subtract 7 from both sides.

 b  + 7 – 7 = 9 – 7

 2

 b  = 2

 2


Step 2:

Multiply both sides by 2 to get the variable by itself.

 2(b)  = 2(2)

    2

b = 4


  Self-check!

Try this!

Try this activity where you will work with two-step equations


Solve for x in the following equation: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨16px¨»«mrow»«mn mathcolor=¨#FFFFFF¨»4«/mn»«mi mathcolor=¨#FFFFFF¨»x«/mi»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mo mathcolor=¨#FFFFFF¨»+«/mo»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mn mathcolor=¨#FFFFFF¨»7«/mn»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mo mathcolor=¨#FFFFFF¨»=«/mo»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mn mathcolor=¨#FFFFFF¨»27«/mn»«/mrow»«/mstyle»«/math»

Step 1: first subtract 7 from both sides

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Step 2: divide by 4 from both sides

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Solve for b in the following equation: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨16px¨»«mrow»«mfrac mathcolor=¨#FFFFFF¨»«mi»b«/mi»«mn»3«/mn»«/mfrac»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mo mathcolor=¨#FFFFFF¨»-«/mo»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mn mathcolor=¨#FFFFFF¨»10«/mn»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mo mathcolor=¨#FFFFFF¨»=«/mo»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mn mathcolor=¨#FFFFFF¨»4«/mn»«/mrow»«/mstyle»«/math»

Step 1: first add 10 to both sides

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Step 2: multiply by 3 to both sides

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Digging Deeper


Click on the Play button below to watch a video on how to solve equations using the two-step method.



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