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9-12 Algebra 2 Unit 4 Lesson 7

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K-5 Math 6-8 Math •9-12 Math

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Algebra 1 Geometry •Algebra 2 Extra Support Materials for Algebra 1

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Unit 1 Unit 2 Unit 3 •Unit 4 Unit 5 Unit 6 Unit 7 Unit 8

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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 Lesson 17 Lesson 18 Lesson 19 Lesson 20

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Unit 3
Unit 4
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Unit 6
Unit 7
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Lesson 6
Lesson 7
Lesson 8
Lesson 9
Lesson 10
Lesson 11
Lesson 12
Lesson 13
Lesson 14
Lesson 15
Lesson 16
Lesson 17
Lesson 18
Lesson 19
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Unit 4, Lesson 7

Inequivalent Equations?

Algebra 2

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 5: Negative Rational Exponents

Select all expressions that are equal to \(\frac{1}{(\sqrt2)^5}\).

\(\text- \frac{5}{\sqrt2}\)
\(\frac{1}{\sqrt{2^5}}\)
\(\frac{1}{\sqrt{32}}\)
\(\text- (\sqrt2)^5\)
\(\text- 2^{\frac52}\)
\(2^{\text- \frac52}\)

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Problem 5

ForLesson 6: Squares and Square Roots

Which are the solutions to the equation \(x^2=36\)?

6 only
-6 only
6 and -6
This equation has no solutions.

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Problem 6

ForLesson 6: Squares and Square Roots

Here is a graph of \(y=x^2\).

<p>Y = x squared graphed on coordinate plane </p>

Use the graph to estimate all solutions to the equation \(x^2=3\).
If you square your estimates, what number should they be close to?
Square your estimates. How close did you get to this number?

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Problem 7

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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Lesson 7 Resources

Student Materials