Justify each step in solving a multi-step equation with variables on one side of the equation.
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This lesson may be extended over more than one day to ensure enough time for both analysis of work and procedural practice.
If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Problems 1 and 2 (benefit from discussion). Find more guidance on adapting our math curriculum for remote learning here.
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Two students, Pablo and Karla, are solving an equation. The equation and their work is shown below.
$${15-3(x-2)+6x=3(13)}$$
Pablo's Work | Karla's Work |
$$15-3x+6+6x=3(13)$$ | $$15-3x+6+6x=39$$ |
$$15+6-3x+6x=3(13)$$ | $$-3x+6x+15+6=39$$ |
$$21+3x=3(13)$$ | $$3x+21=39$$ |
$$3(7+x)=3(13)$$ | $$3x=18$$ |
$$7+x=13$$ | $$x=6$$ |
$$x=6$$ |
Two more students, Christian and Esther, are solving the same equation. They take a different approach to solving the equation, but they each make an error in the first two lines of their work, shown below.
$${15-3(x-2)+6x=3(13)}$$
Christian's Work | Esther's Work |
$$12(x-2)+6x=39$$ | $$15-3x-6+6x=39$$ |
$$12x-24+6x=39$$ | $$15-6-3x+6x=39$$ |
Explain the error that each student made.
Solve the equations.
a. $${-\left ( \frac{1}{2}-15 \right )+\frac{5}{2}x=-2}$$
b. $${\frac{11}{3}=\frac{5}{3}+3\left (\frac{x}{3}+\frac{2}{9} \right )}$$
c. $${2(3m+6)-4(1-2m)=-20}$$
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The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.
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Solve the equation below. For each step, explain why each line of your work is equivalent to the line before it.
$${\frac{1}{2}(-12x+4)+5x=\frac{2}{3}(24)}$$
Find and explain the error in the work below.
$${15=-3(m-2)-9}$$
$${15=-3m+6-9}$$
$${15=-3m-3}$$
$${12=-3m}$$
$${m=-4}$$
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