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Back to Tutor Intake Assessment: Solve rational and radical equations

HSA.REI.A.2 Tutor Intake -- Rational and Radical Equations

This short check helps your tutor understand where to start. Answer each
question without help. If you are not sure, give your best try — the goal
is to find what to work on together, not to grade you.

Grade 9·8 problems·~13 min·Common Core Math - HS Algebra·standard·hsa-rei-a-2
Work through problems with immediate feedback
A

Concepts

1

A student is solving the rational equation xx−3=4x−3\frac{x}{x-3} = \frac{4}{x-3}.

Before doing any algebra, what value of xx must be excluded from the
solution set?

2

A student solves a radical equation and obtains x=4x = 4 and x=−1x = -1.
After checking in the original equation:

  • x=4x = 4: left side =3= 3, right side =3= 3 ✓
  • x=−1x = -1: left side =2= 2, right side =−1= -1 ✗

What is the correct solution set?

3

Why can squaring both sides of a radical equation introduce an extraneous
solution?

B

Procedures

1

Solve the radical equation x+5=4\sqrt{x + 5} = 4.

After solving and checking your answer in the original equation, enter
the value of xx.

2

A student tries to solve x+3=7\sqrt{x} + 3 = 7 by squaring both sides immediately,
writing x+9=49x + 9 = 49.

The student's error is that they squared before   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   . The correct
first step is to subtract 3 from both sides to get x=‾\sqrt{x} = \underline{\hspace{5em}}.

what-was-skipped:
result:
3

Solve the rational equation 3x=12\frac{3}{x} = \frac{1}{2}.

Enter the value of xx.

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