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Algebra 1

Carter, Cuevas, Day, Holiday, Luchin

$Math Studyset Vaia Explanations$ Math

Student Edition · 801 pages

ISBN: 9780078884801

Chapter 11: Q17. (page 728)

State the excluded value for each function.
$y = \frac{3}{3 x - 6}$

Short Answer

Expert verified

Excluded value of the function is $2$ .

Step by step solution

01

Step 1. Exclude the values.

Exclude the values for which $3 x - 6$ equals 0.

$3 x - 6 = 0$

02

Step 2. Add.

Add 6 on each side of the above obtained equation.

$\begin{matrix} 3 x - 6 + 6 = 0 + 6 \\ 3 x = 6 \end{matrix}$

03

Step 3. Divide.

Divide each term by 3.

$\begin{matrix} \frac{3 x}{3} = \frac{6}{3} \\ x = 2 \end{matrix}$

$x$ cannot equal to $2$ . Therefore, the excluded value is $x = 2$ .

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Most popular questions from this chapter

Carl’s father is building a tool chest that is shaped like a rectangular prism. He wants the tool chest to have a surface area of 62 square feet. The height of the chest will be 1 foot shorter than the width. The length will be 3 feet longer than the height.

a. Sketch the model to represent the model.

b. Write a polynomial that represents the surface area of the tool chest.

c. What are the dimensions of the tool chest?

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.

Simplify each expression.

$\frac{\frac{a - 4}{a^{2} + 6 a + 8}}{\frac{a^{2} - 3 a - 4}{a^{2} - a - 6}}$

State whether each sentence is true or false. If false, replace the underlined word, phrase, expression, or number to make a true sentence.

A rational expression has one or more fractions in the numerator and denominator.

Find each product or quotient.

$\frac{3 x - 6}{x^{2} - 9} \cdot \frac{x + 3}{x^{2} - 2 x}$

See all solutions

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