Solve and graph inequalities with variables on both sides 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.
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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.
$$7-{2\over3}x>2+x$$
Solve the inequality.
$${\frac{x-7}{3}\leq \frac{2(x-1)}{8}}$$
Lindsay and Kiana work at the same restaurant. Lindsay earns $12.75 per hour and Kiana, who has been working there longer, earns $15.25 per hour. One week, both girls work the same number of hours at the restaurant, but Lindsay spends $37 and Kiana spends $55. At the end of the week, Lindsay has more money left than Kiana. What is the smallest number of hours the girls could have worked for this to be true?
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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 inequality.
$${\frac{-2x+1}{4}< \frac{3x-6}{6}}$$
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