Question

the expression 3x-10/x-4> 4/9 is an example of A. rational expression . B . rational functions . C. rational equation D. rational inequality .​

Answer 1

Answer:

The correct answer is option (d) Rational inequality

Step-by-step explanation:

The given expression is,

$\frac{3x-10}{x-4} > \frac{4}{9}$

The inequality which contains the rational expression, where the rational expression is expressed in the ratio of two polynomials.

The rational expression is given in the form of,

$\frac{R(x)}{Q(x)} > 0$

> can also be replaced by ≤ or ≥ or <

Where the polynomials are R(x) and Q(x), and Q(x) will not be zero.

Therefore, the given expression can be written as:

$\frac{3x-10}{x-4} - \frac{4}{9} = 0$

Steps to solve rational inequality:

Step 1 : Write the inequality in general form.

Step 2: Solve the equation by setting the numerator and denominator to zero and the critical values will be obtained.

The function is zero when the numerator is zero and the function is undefined when the denominator is zero.

Step 3: In the number line the critical values are plotted and the line is separated using the limits.

Step 4: The test number was taken from each interval and was plugged into original equality.

• If the statement is true, the interval was came from the solution.
• If the statement is false, the interval was not came from the solution.

Step 5: It is determined whether the endpoints in the intervals from the solution include the intervals.

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