# How To Solve A Rational Inequality

## Which is a correct first step in solving the inequality?

Answer: The first step in solving the given inequality is to use the distributive property and open the brackets that is -8x + 4 > 5 – 3x.

## How do you solve rational inequalities step by step?

To solve a rational inequality we follow these steps:

1. Put the inequality in general form.
2. Set the numerator and denominator equal to zero and solve. …
3. Plot the critical values on a number line breaking the number line into intervals.
4. Take a test number from each interval and plug it into the original inequality.

## How are rational inequalities solved?

To solve a rational inequality you first find the zeroes (from the numerator) and the undefined points (from the denominator). You use these zeroes and undefined points to divide the number line into intervals. Then you find the sign of the rational on each interval.

## What are 5 examples of rational equation?

Solving Rational Equations

• 4/x + 5/2 = -11/x.
• 5x/(x – 2) = 7 + 10/(x – 2)
• (3x – 2)/(x – 2) = 6/(x2 – 4) + 1.
• 2/(x2 – x) = 1/(x – 1)
• 3/(x + 2) = 6/(x – 1)

## What is the formula for rational equation?

A rational equation is an equation containing at least one fraction whose numerator and denominator are polynomials frac{P(x)}{Q(x)}. Q(x)P(x). These fractions may be on one or both sides of the equation.

## What are the 5 example of rational inequality?

Inequalities

Symbol Words Example
> greater than (x+1)/(3−x) > 2
< less than x/(x+7) < −3
greater than or equal to (x−1)/(5−x) ≥ 0
less than or equal to (3−2x)/(x−1) ≤ 2

## What is rational inequality formula?

Rational Inequality. A rational inequality is an inequality that contains a rational expression. Inequalities such as32x>1 2xx−3<4 2x−3x−6≥x and 14−2×2≤3x are rational inequalities as they each contain a rational expression.

## How To Solve A Rational Inequality?

0:0010:17 Rational Inequalities – YouTubeYouTubeStart of suggested clipEnd of suggested clipSo let’s start with a number line. Now we need to set the numerator equal to zero so X is equal toMoreSo let’s start with a number line. Now we need to set the numerator equal to zero so X is equal to three. And if we set the denominator equal to zero.See also what are some benefits and consequences of modern farming techniques

A quadratic inequality is an equation of second degree that uses an inequality sign instead of an equal sign. Examples of quadratic inequalities are: x2 – 6x – 16 ≤ 0 2x2 – 11x + 12 > 0 x2 + 4 > 0 x2 – 3x + 2 ≤ 0 etc. Solving a quadratic inequality in Algebra is similar to solving a quadratic equation.

## How do you find complex solutions?

To solve for the complex solutions of an equation you use factoring the square root property for solving quadratics and the quadratic formula.

Following are answers to the practice questions:

1. The answer is x = 3i –3i. Add –9 to each side to get x2 = –9. …
4. The answer is x= 2 –2 4i –4i.

## How do you find the critical value of a rational inequality?

The key approach in solving rational inequalities relies on finding the critical values of the rational expression which divide the number line into distinct open intervals. The critical values are simply the zeros of both the numerator and the denominator.

## How many solutions are there for a rational equation?

equal to itself this equation is an identity. That means we have infinitely many solutions. The only value that will not make this equation true is any number that results in a denominator of zero.

## What is solving an inequality?

To ‘solve’ an inequality means to find a range or ranges of values that an unknown x can take and still satisfy the inequality. In this unit inequalities are solved by using algebra and by using graphs.

## What equations have real rational?

When a b and c are real numbers a ≠ 0 and the discriminant is positive and perfect square then the roots α and β of the quadratic equation ax2 + bx + c = 0 are real rational and unequal.

## What is the first step in solving a rational function?

Finding Solutions to Rational Equations The first step in solving rational equations is to transform the equation into a polynomial equation. This is accomplished by clearing the fraction which means multiplying the entire equation by the common denominator of all the rational expressions.

## Which equation has no solution?

The constants are the numbers alone with no variables. If the coefficients are the same on both sides then the sides will not equal therefore no solutions will occur. Use distributive property on the right side first.

## What is a rational solution?

1 using reason or logic in thinking out a problem. 2 in accordance with the principles of logic or reason reasonable.

## What is real and unequal roots?

When discriminant is greater than zero the roots are unequal and real. When discriminant is equal to zero the roots are equal and real. When discriminant is less than zero the roots are imaginary.