Chapter 11: Q6. (page 727)

State whether each sentence is true or false. If false, replace the underlined word, phrase, expression, or number to make a true sentence.
The equation $\frac{3 x}{x - 2} = \frac{6}{x - 2}$ has an extraneous solution, 2.

Short Answer

Expert verified

The given statement is True.

Step by step solution

Step 1. State the concept of extraneous solution.

When a solution of a rational equation results in a zero in the denominator, that solution must be excluded. Such solutions are called extraneous solutions.

Step 2. Explanation of the statement.

The given equation is $\frac{3 x}{x - 2} = \frac{6}{x - 2}$ . On solving further, the solution thus obtained is:

$\frac{3 x}{x - 2} = \frac{6}{x - 2} 3 x = 6 x = 2$

Step 3. Write whether the statement is true or false.

But $x = 2$ results in a zero in the denominator of the original equation. Therefore, $x = 2$ is an extraneous solution.

The given statement “The equation $\frac{3 x}{x - 2} = \frac{6}{x - 2}$ has an extraneous solution, 2.” is true.

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$x$	1	4	8	12
$y$	2	8	16	24

State whether each sentence is true or false. If false, replace the underlined word, phrase, expression, or number to make a true sentence.
The equation $\frac{3 x}{x - 2} = \frac{6}{x - 2}$ has an extraneous solution, 2.

Short Answer

Step by step solution

Step 1. State the concept of extraneous solution.

Step 2. Explanation of the statement.

Step 3. Write whether the statement is true or false.

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State whether each sentence is true or false. If false, replace the underlined word, phrase, expression, or number to make a true sentence.The equation3xx−2=6x−2 has an extraneous solution, 2.

Short Answer

Step by step solution

Step 1. State the concept of extraneous solution.

Step 2. Explanation of the statement.

Step 3. Write whether the statement is true or false.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Probability and Statistics

Theoretical and Mathematical Physics

Statistics

Calculus

Geometry

Study anywhere. Anytime. Across all devices.

State whether each sentence is true or false. If false, replace the underlined word, phrase, expression, or number to make a true sentence.
The equation $\frac{3 x}{x - 2} = \frac{6}{x - 2}$ has an extraneous solution, 2.