Lesson 9 — Activity 2: Two-Step Equations
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
b + 7 = 9
2
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
«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=¨#62D3B3¨»-«/mo»«mo mathcolor=¨#62D3B3¨»§#160;«/mo»«mn mathcolor=¨#62D3B3¨»7«/mn»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mo mathcolor=¨#FFFFFF¨»=«/mo»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mn mathcolor=¨#FFFFFF¨»27«/mn»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mo mathcolor=¨#62D3B3¨»-«/mo»«mo mathcolor=¨#62D3B3¨»§#160;«/mo»«mn mathcolor=¨#62D3B3¨»7«/mn»«/mrow»«/mstyle»«/math»
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«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn mathcolor=¨#FFFFFF¨ mathsize=¨16px¨»4«/mn»«mi mathcolor=¨#FFFFFF¨ mathsize=¨16px¨»x«/mi»«mo mathcolor=¨#FFFFFF¨ mathsize=¨16px¨»§#160;«/mo»«mo mathcolor=¨#FFFFFF¨ mathsize=¨16px¨»=«/mo»«mo mathcolor=¨#FFFFFF¨ mathsize=¨16px¨»§#160;«/mo»«mn mathcolor=¨#FFFFFF¨ mathsize=¨16px¨»20«/mn»«/math»
Step 2: divide by 4 from both sides
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«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac mathcolor=¨#FFFFFF¨»«mrow»«menclose notation=¨updiagonalstrike¨»«mn mathsize=¨16px¨»4«/mn»«/menclose»«mi mathsize=¨16px¨»x«/mi»«/mrow»«menclose notation=¨updiagonalstrike¨»«mn mathsize=¨16px¨»4«/mn»«/menclose»«/mfrac»«mo mathcolor=¨#FFFFFF¨ mathsize=¨16px¨»§#160;«/mo»«mo mathcolor=¨#FFFFFF¨ mathsize=¨16px¨»=«/mo»«mo mathcolor=¨#FFFFFF¨ mathsize=¨16px¨»§#160;«/mo»«mfrac mathcolor=¨#FFFFFF¨»«mn mathsize=¨16px¨»20«/mn»«mn mathsize=¨16px¨»4«/mn»«/mfrac»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨16px¨»«mrow»«mi mathcolor=¨#FFFFFF¨»x«/mi»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mo mathcolor=¨#FFFFFF¨»=«/mo»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mn mathcolor=¨#FFFFFF¨»5«/mn»«/mrow»«/mstyle»«/math»
Step 1: first subtract 7 from both sides
«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=¨#62D3B3¨»-«/mo»«mo mathcolor=¨#62D3B3¨»§#160;«/mo»«mn mathcolor=¨#62D3B3¨»7«/mn»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mo mathcolor=¨#FFFFFF¨»=«/mo»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mn mathcolor=¨#FFFFFF¨»27«/mn»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mo mathcolor=¨#62D3B3¨»-«/mo»«mo mathcolor=¨#62D3B3¨»§#160;«/mo»«mn mathcolor=¨#62D3B3¨»7«/mn»«/mrow»«/mstyle»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn mathcolor=¨#FFFFFF¨ mathsize=¨16px¨»4«/mn»«mi mathcolor=¨#FFFFFF¨ mathsize=¨16px¨»x«/mi»«mo mathcolor=¨#FFFFFF¨ mathsize=¨16px¨»§#160;«/mo»«menclose mathcolor=¨#FFFFFF¨ notation=¨updiagonalstrike¨»«mo mathsize=¨16px¨»+«/mo»«mo mathsize=¨16px¨»§#160;«/mo»«mn mathsize=¨16px¨»7«/mn»«/menclose»«mo mathcolor=¨#FFFFFF¨ mathsize=¨16px¨»§#160;«/mo»«menclose mathcolor=¨#FFFFFF¨ notation=¨updiagonalstrike¨»«mo mathsize=¨16px¨»-«/mo»«mo mathsize=¨16px¨»§#160;«/mo»«mn mathsize=¨16px¨»7«/mn»«/menclose»«mo mathcolor=¨#FFFFFF¨ mathsize=¨16px¨»§#160;«/mo»«mo mathcolor=¨#FFFFFF¨ mathsize=¨16px¨»=«/mo»«mo mathcolor=¨#FFFFFF¨ mathsize=¨16px¨»§#160;«/mo»«mn mathcolor=¨#FFFFFF¨ mathsize=¨16px¨»27«/mn»«mo mathcolor=¨#FFFFFF¨ mathsize=¨16px¨»§#160;«/mo»«mo mathcolor=¨#FFFFFF¨ mathsize=¨16px¨»-«/mo»«mo mathcolor=¨#FFFFFF¨ mathsize=¨16px¨»§#160;«/mo»«mn mathcolor=¨#FFFFFF¨ mathsize=¨16px¨»7«/mn»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn mathcolor=¨#FFFFFF¨ mathsize=¨16px¨»4«/mn»«mi mathcolor=¨#FFFFFF¨ mathsize=¨16px¨»x«/mi»«mo mathcolor=¨#FFFFFF¨ mathsize=¨16px¨»§#160;«/mo»«mo mathcolor=¨#FFFFFF¨ mathsize=¨16px¨»=«/mo»«mo mathcolor=¨#FFFFFF¨ mathsize=¨16px¨»§#160;«/mo»«mn mathcolor=¨#FFFFFF¨ mathsize=¨16px¨»20«/mn»«/math»
Step 2: divide by 4 from both sides
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨16px¨»«mrow»«mfrac mathcolor=¨#62D3B3¨»«mrow»«mn mathcolor=¨#FFFFFF¨»4«/mn»«mi mathcolor=¨#FFFFFF¨»x«/mi»«/mrow»«mn»4«/mn»«/mfrac»«mo mathcolor=¨#62D3B3¨»§#160;«/mo»«mo mathcolor=¨#FFFFFF¨»=«/mo»«mo mathcolor=¨#62D3B3¨»§#160;«/mo»«mfrac mathcolor=¨#62D3B3¨»«mn mathcolor=¨#FFFFFF¨»20«/mn»«mn»4«/mn»«/mfrac»«/mrow»«/mstyle»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac mathcolor=¨#FFFFFF¨»«mrow»«menclose notation=¨updiagonalstrike¨»«mn mathsize=¨16px¨»4«/mn»«/menclose»«mi mathsize=¨16px¨»x«/mi»«/mrow»«menclose notation=¨updiagonalstrike¨»«mn mathsize=¨16px¨»4«/mn»«/menclose»«/mfrac»«mo mathcolor=¨#FFFFFF¨ mathsize=¨16px¨»§#160;«/mo»«mo mathcolor=¨#FFFFFF¨ mathsize=¨16px¨»=«/mo»«mo mathcolor=¨#FFFFFF¨ mathsize=¨16px¨»§#160;«/mo»«mfrac mathcolor=¨#FFFFFF¨»«mn mathsize=¨16px¨»20«/mn»«mn mathsize=¨16px¨»4«/mn»«/mfrac»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨16px¨»«mrow»«mi mathcolor=¨#FFFFFF¨»x«/mi»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mo mathcolor=¨#FFFFFF¨»=«/mo»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mn mathcolor=¨#FFFFFF¨»5«/mn»«/mrow»«/mstyle»«/math»
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
«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=¨#62D3B3¨»+«/mo»«mo mathcolor=¨#62D3B3¨»§#160;«/mo»«mn mathcolor=¨#62D3B3¨»10«/mn»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mo mathcolor=¨#FFFFFF¨»=«/mo»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mn mathcolor=¨#FFFFFF¨»4«/mn»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mo mathcolor=¨#62D3B3¨»+«/mo»«mo mathcolor=¨#62D3B3¨»§#160;«/mo»«mn mathcolor=¨#62D3B3¨»10«/mn»«/mrow»«/mstyle»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac mathcolor=¨#FFFFFF¨»«mi mathsize=¨16px¨»b«/mi»«mn mathsize=¨16px¨»3«/mn»«/mfrac»«mo mathcolor=¨#FFFFFF¨ mathsize=¨16px¨»§#160;«/mo»«menclose mathcolor=¨#FFFFFF¨ notation=¨updiagonalstrike¨»«mo mathsize=¨16px¨»-«/mo»«mo mathsize=¨16px¨»§#160;«/mo»«mn mathsize=¨16px¨»10«/mn»«mo mathsize=¨16px¨»§#160;«/mo»«/menclose»«menclose mathcolor=¨#FFFFFF¨ notation=¨updiagonalstrike¨»«mo mathsize=¨16px¨»+«/mo»«mo mathsize=¨16px¨»§#160;«/mo»«mn mathsize=¨16px¨»10«/mn»«mo mathsize=¨16px¨»§#160;«/mo»«/menclose»«mo mathcolor=¨#FFFFFF¨ mathsize=¨16px¨»=«/mo»«mo mathcolor=¨#FFFFFF¨ mathsize=¨16px¨»§#160;«/mo»«mn mathcolor=¨#FFFFFF¨ mathsize=¨16px¨»4«/mn»«mo mathcolor=¨#FFFFFF¨ mathsize=¨16px¨»§#160;«/mo»«mo mathcolor=¨#FFFFFF¨ mathsize=¨16px¨»+«/mo»«mo mathcolor=¨#FFFFFF¨ mathsize=¨16px¨»§#160;«/mo»«mn mathcolor=¨#FFFFFF¨ mathsize=¨16px¨»10«/mn»«/math»
«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¨»14«/mn»«/mrow»«/mstyle»«/math»
Step 2: multiply by 3 to both sides
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«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mrow mathcolor=¨#FFFFFF¨»«mfrac»«mrow»«menclose notation=¨updiagonalstrike¨»«mo mathsize=¨16px¨»(«/mo»«mn mathsize=¨16px¨»3«/mn»«mo mathsize=¨16px¨»)«/mo»«/menclose»«mi mathsize=¨16px¨»b«/mi»«/mrow»«menclose notation=¨updiagonalstrike¨»«mn mathsize=¨16px¨»3«/mn»«/menclose»«/mfrac»«mo mathsize=¨16px¨»§#160;«/mo»«mo mathsize=¨16px¨»=«/mo»«mo mathsize=¨16px¨»§#160;«/mo»«mn mathsize=¨16px¨»14«/mn»«mo mathsize=¨16px¨»(«/mo»«mn mathsize=¨16px¨»3«/mn»«mo mathsize=¨16px¨»)«/mo»«/mrow»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨16px¨»«mrow»«mi mathcolor=¨#FFFFFF¨»b«/mi»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mo mathcolor=¨#FFFFFF¨»=«/mo»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mn mathcolor=¨#FFFFFF¨»42«/mn»«/mrow»«/mstyle»«/math»
Step 1: first add 10 to both sides
«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=¨#62D3B3¨»+«/mo»«mo mathcolor=¨#62D3B3¨»§#160;«/mo»«mn mathcolor=¨#62D3B3¨»10«/mn»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mo mathcolor=¨#FFFFFF¨»=«/mo»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mn mathcolor=¨#FFFFFF¨»4«/mn»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mo mathcolor=¨#62D3B3¨»+«/mo»«mo mathcolor=¨#62D3B3¨»§#160;«/mo»«mn mathcolor=¨#62D3B3¨»10«/mn»«/mrow»«/mstyle»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac mathcolor=¨#FFFFFF¨»«mi mathsize=¨16px¨»b«/mi»«mn mathsize=¨16px¨»3«/mn»«/mfrac»«mo mathcolor=¨#FFFFFF¨ mathsize=¨16px¨»§#160;«/mo»«menclose mathcolor=¨#FFFFFF¨ notation=¨updiagonalstrike¨»«mo mathsize=¨16px¨»-«/mo»«mo mathsize=¨16px¨»§#160;«/mo»«mn mathsize=¨16px¨»10«/mn»«mo mathsize=¨16px¨»§#160;«/mo»«/menclose»«menclose mathcolor=¨#FFFFFF¨ notation=¨updiagonalstrike¨»«mo mathsize=¨16px¨»+«/mo»«mo mathsize=¨16px¨»§#160;«/mo»«mn mathsize=¨16px¨»10«/mn»«mo mathsize=¨16px¨»§#160;«/mo»«/menclose»«mo mathcolor=¨#FFFFFF¨ mathsize=¨16px¨»=«/mo»«mo mathcolor=¨#FFFFFF¨ mathsize=¨16px¨»§#160;«/mo»«mn mathcolor=¨#FFFFFF¨ mathsize=¨16px¨»4«/mn»«mo mathcolor=¨#FFFFFF¨ mathsize=¨16px¨»§#160;«/mo»«mo mathcolor=¨#FFFFFF¨ mathsize=¨16px¨»+«/mo»«mo mathcolor=¨#FFFFFF¨ mathsize=¨16px¨»§#160;«/mo»«mn mathcolor=¨#FFFFFF¨ mathsize=¨16px¨»10«/mn»«/math»
«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¨»14«/mn»«/mrow»«/mstyle»«/math»
Step 2: multiply by 3 to both sides
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨16px¨»«mrow»«mfrac mathcolor=¨#FFFFFF¨»«mrow»«mo mathcolor=¨#62D3B3¨»(«/mo»«mn mathcolor=¨#62D3B3¨»3«/mn»«mo mathcolor=¨#62D3B3¨»)«/mo»«mi»b«/mi»«/mrow»«mn»3«/mn»«/mfrac»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mo mathcolor=¨#FFFFFF¨»=«/mo»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mn mathcolor=¨#FFFFFF¨»14«/mn»«mo mathcolor=¨#62D3B3¨»(«/mo»«mn mathcolor=¨#62D3B3¨»3«/mn»«mo mathcolor=¨#62D3B3¨»)«/mo»«/mrow»«/mstyle»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mrow mathcolor=¨#FFFFFF¨»«mfrac»«mrow»«menclose notation=¨updiagonalstrike¨»«mo mathsize=¨16px¨»(«/mo»«mn mathsize=¨16px¨»3«/mn»«mo mathsize=¨16px¨»)«/mo»«/menclose»«mi mathsize=¨16px¨»b«/mi»«/mrow»«menclose notation=¨updiagonalstrike¨»«mn mathsize=¨16px¨»3«/mn»«/menclose»«/mfrac»«mo mathsize=¨16px¨»§#160;«/mo»«mo mathsize=¨16px¨»=«/mo»«mo mathsize=¨16px¨»§#160;«/mo»«mn mathsize=¨16px¨»14«/mn»«mo mathsize=¨16px¨»(«/mo»«mn mathsize=¨16px¨»3«/mn»«mo mathsize=¨16px¨»)«/mo»«/mrow»«/math»
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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.