Rational Inequalities 5/4-4/(3y)<=4/2

Divide by .
Move all terms not containing to the right side of the inequality.
Subtract from both sides of the inequality.
Simplify the right side of the inequality.
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Combine.
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
Multiply by .
Subtract from .
Solve for .
Multiply each term by and simplify.
Multiply each term in by .
Simplify the left side of the inequality by cancelling the common factors.
Cancel the common factor of .
Move the leading negative in into the numerator.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Move the negative in front of the fraction.
Combine and .
Move to the left side of the equation by subtracting it from both sides.
Find the LCD of the terms in the equation.
To find the LCD of a set of numbers , find the LCM of the denominators.
Calculate the LCM of first two denominators in the list, and .
Find the values of the numerical part of each term. Select the largest one, which in this case is . Multiply them together to get the current total. In this case, the current total is .
Current Total =
Multiply the numeric part of the denominators together.
Current Total =
Multiply the numeric part of the denominators together.
Current Total =
Check each value in the numerical part of each term against the current total. Since the current total is evenly divisible, return it. That is the least common denominator of the numerical part of the fraction.
Multiply each term by and simplify.
Multiply each term in by .
Simplify each term.
Cancel the common factor of .
Move the leading negative in into the numerator.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Multiply by .
Cancel the common factor of .
Move the leading negative in into the numerator.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Multiply by .
Multiply by .
Add to both sides of the inequality.
Divide each term by and simplify.
Divide each term in by . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.
Cancel the common factor of .
Cancel the common factor.
Divide by .
Move the negative in front of the fraction.
Find the domain of .
Set the denominator in equal to to find where the expression is undefined.
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Divide by .
The domain is all values of that make the expression defined.
Interval Notation:
Interval Notation:
Use each root to create test intervals.
Choose a test value from each interval and plug this value into the original inequality to determine which intervals satisfy the inequality.
Test a value on the interval to see if it makes the inequality true.
Choose a value on the interval and see if this value makes the original inequality true.
Replace with in the original inequality.
The left side is less than the right side , which means that the given statement is always true.
True
True
Test a value on the interval to see if it makes the inequality true.
Choose a value on the interval and see if this value makes the original inequality true.
Replace with in the original inequality.
The left side is greater than the right side , which means that the given statement is false.
False
False
Test a value on the interval to see if it makes the inequality true.
Choose a value on the interval and see if this value makes the original inequality true.
Replace with in the original inequality.
The left side is less than the right side , which means that the given statement is always true.
True
True
Compare the intervals to determine which ones satisfy the original inequality.
True
False
True
True
False
True
The solution consists of all of the true intervals.
or
The result can be shown in multiple forms.
Inequality Form:
Interval Notation:
Rational Inequalities 5/4-4/(3y)<=4/2