Question 1

Which of the following correctly identifies a rational expression?

Accepted Answer

A ratio of two polynomials.

Answer

An expression involving only whole numbers.

Answer

An equation with no variables.

Answer

An inequality with no fractions.

Question 2

Which of these is a rational inequality?

Accepted Answer

(x+3)/(x−2)>0

Answer

x + 7 < 3

Answer

(2x−5)/(x+1)=3

Answer

x^2 + 4x − 5 = 0

Question 3

What distinguishes a rational equation from a rational inequality?

Accepted Answer

A rational equation involves an equality symbol, while a rational inequality uses inequality signs.

Answer

A rational equation involves polynomials, while rational inequalities do not.

Answer

Rational equations can only be solved graphically.

Answer

A rational equation always has a graph.

Question 4

What is the first step in solving the equation (x+1)/(x−3)=4?

Accepted Answer

Multiply through by the least common denominator (LCD).

Answer

Factor the denominator.

Answer

Simplify both sides.

Answer

Add 3 to both sides.

Question 5

Why must we exclude certain values when solving the inequality (3x−2)/(x+1)>0?

Accepted Answer

They make the denominator undefined.

Answer

They are extraneous solutions.

Answer

They violate the inequality rules.

Answer

They make the numerator equal to zero.

Question 6

In solving the inequality (x−4)/(2x+3)<0, how do critical values help?

Accepted Answer

They divide the number line into testable intervals.

Answer

They make the inequality true.

Answer

They provide the endpoints of the solution set.

Answer

They give the exact solutions.

Question 7

Why is x=0 excluded in the equation 3/(x+2)=6/x?

Accepted Answer

x=0 results in division by zero.

Answer

x=0 is an extraneous solution.

Answer

x=0 satisfies the equation.

Answer

x=0 changes the inequality direction.

Question 8

What does the solution to (x+1)/(x−2)=3 exclude?

Accepted Answer

Solutions where the denominator is zero.

Answer

Solutions where the numerator is zero.

Answer

Solutions where the variable is negative.

Answer

Solutions where the inequality changes direction.

Question 9

Solve the equation 2/x=8. What is x?

Accepted Answer

x=1/4

Answer

x=1/8

Answer

x=4

Answer

x=16

Question 10

Solve (x+5)/(x−2)=2. What is x?

Accepted Answer

x=9

Answer

x=−7

Answer

x=2

Answer

x=19

Question 11

When solving the inequality , what should you consider about the values of x that make the denominator zero?

Accepted Answer

These values are not included in the solution because they make the expression undefined.

Answer

These values have no impact on the solution.

Answer

These values are solutions to the inequality.

Answer

These values indicate where the inequality is equal to zero.

Question 12

In the equation ,why do we exclude x=5 from potential solutions?

Accepted Answer

Because x=5 results in an undefined expression

Answer

Because x=5 changes the inequality direction..

Answer

Because x=5 results in a zero in the numerator.

Answer

Because x=5 leads to an extraneous solution.

Question 13

What is the solution to $\frac{2}{x}=10$ ?

Accepted Answer

1/5

Answer

5

Answer

1/2

Answer

20

Question 14

Solve the equation $\frac{2}{x}=10$ .What is x?

Accepted Answer

x = 6

Answer

x = 1/2

Answer

x = 20

Answer

x = -1

Question 15

In the equation $\frac{2}{x}=10$ ,why do we exclude x=8 from potential solutions?

Accepted Answer

Because x=8 results in an undefined expression

Answer

Because x=5 leads to an extraneous solution.

Answer

Because x=5 results in a zero in the numerator.

Answer

Because x=5 changes the inequality direction..

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