Solve and graph inequalities with variables on one side of the inequality.
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Lessons 11 and 12 extend on 7.EE.4b and bridge a gap to high school standard A.REI.3. Inequalities are not included in the 8th grade standards, but this is a natural extension of students’ work with equations from earlier in the unit, especially now that students are able to work with more complex equations and inequalities. These two lessons can be treated as optional.
If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Problem 1 or 2 (benefit from worked example). Note, this is beyond 8th grade expectations, bridging a gap between 7th grade and HS; this lesson may be skipped. Find more guidance on adapting our math curriculum for remote learning here.
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Solve the inequality. Then pick a value for $$x$$ and check your answer. Lastly, graph your solution on a number line.
$$8-4(x-2)+6(x-1)>20$$
Solve the inequality.
$${4-{x\over3}\leq {3\over4}(32)}$$
Noah is creating a rectangular picture frame out of wood. He wants the width of the frame to be 6 inches less than half the length. If Noah has a total of 60 inches of wood that he can use for the frame, write and solve an inequality to represent the possible measurements of the length of the frame.
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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 each inequality, then represent the solutions on a number line.
a. $${{{-2x+4}\over5} \geq 18}$$
b. $${{3\over5}(10-15x)+13x > -20}$$