Solve and reason with equations with three types of solutions.
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In this lesson, students use what they know about equations with no, infinite, or unique solutions to reason about solutions without having to completely solve the equation. For example, if they can simplify each side of an equation to one or two terms, they should be able to determine if a solution is possible and if so, if that solution is unique (MP.7).
If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Problem 1 or 2 (benefit from worked example). Find more guidance on adapting our math curriculum for remote learning here.
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The equation below has a unique solution.
$${2(3x-4)-(x-7)=-6(x+1)+7x}$$
The equation below is incomplete.
$${{1\over3}(2{x+}18-3)+x=}$$ _____ $${x+}$$ _____
Complete the equation, by filling in the blanks, to create an equation with:
Without solving them, say whether these equations have a positive solution, a negative solution, a zero solution, or no solution.
a. $${3x=5}$$
b. $${5z+7=3}$$
c. $${7-5w=3}$$
d. $${4a=9a}$$
e. $${y=y+1}$$
The Sign of Solutions, accessed on Aug. 31, 2017, 3:33 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.
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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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The left side of an equation is shown below.
$${-x-7+6\left ( {1\over2}x+2{1\over2} \right )=}$$ _________________
Each expression below can be placed on the right side of the equation to complete the equation.
$${2(x+4)}$$
$${2({x+8})}$$
$${2x+15}$$
$${-2{x+8}}$$
$${x+8}$$
$${8+2x}$$
Which expressions, when placed on the right side of the equation, create an equation with: