Understand that equations can have no solutions, infinite solutions, or a unique solution; classify equations by their solution.
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Lessons 8 and 9 introduce students to the three types of solutions that an equation can have. This lesson focuses on students understanding what each solution means about the equation, and on becoming familiar with arriving at solutions that look like $${4=2}$$ or $${8=8}$$ (MP.2). In the next lesson, students will reason with all three types of solutions to further internalize what they mean. The concept of no solution, infinite solutions, and unique solution will reappear when students study systems of linear equations in Unit 6.
If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Problem 1 (benefits from discussion) and Anchor Problem 2 (benefits from worked example). Find more guidance on adapting our math curriculum for remote learning here.
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These scales are all currently balanced. You must choose a number to fill into the boxes in each problem that will keep them balanced. In each individual box you may only use one number.
Solving Special Case Equations is made available on Everybody is a Genius under the CC BYNCSA 3.0 US license. Accessed Aug. 31, 2017, 2:41 p.m..
Sort the equations below into the three categories.
a. $${3x=0}$$
b. $${3x=2x}$$
c. $${3x=2x}+x$$
d. $${2x+1=2x+2}$$
e. $${3x1=2x1}$$
f. $${x+2=2+x}$$
g. $${x+2=x2}$$
h. $${2x3=32x}$$
Infinite Solutions  Unique Solution  No Solution 

Solve the equations below and explain what each solution means.
a. $${5x2\left ({1\over2}+x \right ) + 8 =  {1\over4}(1612x)}$$
b. $${1.6(x+4)3(0.2x+1)=2x{1\over2}(18.6)}$$
c. $${{{{1\over2}x +4}\over1} = {{x8}\over2}}$$
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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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Todd and Jason both solved an equation and ended up with this final line in their work: $${{2}x=4x}$$.
Do you agree with either Todd or Jason? Explain your reasoning.
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