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9-12 Integrated Math 3 Unit 3 Lesson 8

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K-5 Math 6-8 Math •9-12 Math

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Integrated Math 1 Integrated Math 2 •Integrated Math 3

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Unit 1 Unit 2 •Unit 3 Unit 4 Unit 5 Unit 6 Unit 7

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Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 Lesson 7 •Lesson 8 Lesson 9 Lesson 10 Lesson 11 Lesson 12 Lesson 13 Lesson 14 Lesson 15 Lesson 16

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Unit 3, Lesson 8

Inequivalent Equations?

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Integrated Math 3

Practice

Problem 1

Noah solved the equation \(5x^2=45\). Here are his steps:

\(\begin{align} 5x^2 &= 45 \\ x^2 &= 9 \\ x &= 3 \\ \end{align}\)

Do you agree with Noah? Explain your reasoning.

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Problem 2

Find the solution(s) to each equation, or explain why there is no solution.

\(\sqrt{x+4}+7=5\)
\(\sqrt{47-x}-2 = 4\)
\(\frac12 \sqrt{20+x} = 5\)

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Problem 3

Which is a solution to the equation \(\sqrt{5-x}+13=4\)?

86
81
9
The equation has no solution.

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Problem 4

ForLesson 12: Polynomial Division (Part 1)

The polynomial function \(q(x)=3x^3+11x^2-14x-40\) has a known factor of \((3x + 5)\). Rewrite \(q(x)\) as the product of linear factors.

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Problem 5

ForLesson 11: Finding Intersections

What are the solutions to the equation \((x-1)(x+2)=\text-2\)?

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Problem 6

ForLesson 12: Cross-Sections and Volume

This solid has curved sides. All cross sections parallel to the base are squares measuring 3 units on each side. The height from the base to the top is 8 units. What is the volume of this solid?

<p>Solid with curved sides. Top and bottom bases are squares, side lengths = 3.</p>

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Lesson 8 Resources

Student Materials