Lesson 7

Inequivalent Equations

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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.

Solution

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Problem 2

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

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

Solution

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Problem 3

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

A:

86

B:

81

C:

9

D:

The equation has no solution.

Solution

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Problem 4

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

A:

\(\text- \frac{5}{\sqrt2}\)

B:

\(\frac{1}{\sqrt{2^5}}\)

C:

\(\frac{1}{\sqrt{32}}\)

D:

\(\text- (\sqrt2)^5\)

E:

\(\text- 2^{\frac52}\)

F:

\(2^{\text- \frac52}\)

Solution

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(From Unit 3, Lesson 5.)

Problem 5

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

A:

6 only

B:

-6 only

C:

6 and -6

D:

This equation has no solutions.

Solution

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(From Unit 3, Lesson 6.)

Problem 6

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

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

Solution

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(From Unit 3, Lesson 6.)

Problem 7

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.

Solution

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(From Unit 2, Lesson 12.)