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.
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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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