Basic Math Examples

Simplify 20x^2-9x>=20
Step 1
Convert the inequality to an equation.
Step 2
Subtract from both sides of the equation.
Step 3
Factor by grouping.
Tap for more steps...
Step 3.1
For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is .
Tap for more steps...
Step 3.1.1
Factor out of .
Step 3.1.2
Rewrite as plus
Step 3.1.3
Apply the distributive property.
Step 3.2
Factor out the greatest common factor from each group.
Tap for more steps...
Step 3.2.1
Group the first two terms and the last two terms.
Step 3.2.2
Factor out the greatest common factor (GCF) from each group.
Step 3.3
Factor the polynomial by factoring out the greatest common factor, .
Step 4
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 5
Set equal to and solve for .
Tap for more steps...
Step 5.1
Set equal to .
Step 5.2
Solve for .
Tap for more steps...
Step 5.2.1
Subtract from both sides of the equation.
Step 5.2.2
Divide each term in by and simplify.
Tap for more steps...
Step 5.2.2.1
Divide each term in by .
Step 5.2.2.2
Simplify the left side.
Tap for more steps...
Step 5.2.2.2.1
Cancel the common factor of .
Tap for more steps...
Step 5.2.2.2.1.1
Cancel the common factor.
Step 5.2.2.2.1.2
Divide by .
Step 5.2.2.3
Simplify the right side.
Tap for more steps...
Step 5.2.2.3.1
Move the negative in front of the fraction.
Step 6
Set equal to and solve for .
Tap for more steps...
Step 6.1
Set equal to .
Step 6.2
Solve for .
Tap for more steps...
Step 6.2.1
Add to both sides of the equation.
Step 6.2.2
Divide each term in by and simplify.
Tap for more steps...
Step 6.2.2.1
Divide each term in by .
Step 6.2.2.2
Simplify the left side.
Tap for more steps...
Step 6.2.2.2.1
Cancel the common factor of .
Tap for more steps...
Step 6.2.2.2.1.1
Cancel the common factor.
Step 6.2.2.2.1.2
Divide by .
Step 7
The final solution is all the values that make true.
Step 8
Use each root to create test intervals.
Step 9
Choose a test value from each interval and plug this value into the original inequality to determine which intervals satisfy the inequality.
Tap for more steps...
Step 9.1
Test a value on the interval to see if it makes the inequality true.
Tap for more steps...
Step 9.1.1
Choose a value on the interval and see if this value makes the original inequality true.
Step 9.1.2
Replace with in the original inequality.
Step 9.1.3
The left side is greater than the right side , which means that the given statement is always true.
True
True
Step 9.2
Test a value on the interval to see if it makes the inequality true.
Tap for more steps...
Step 9.2.1
Choose a value on the interval and see if this value makes the original inequality true.
Step 9.2.2
Replace with in the original inequality.
Step 9.2.3
The left side is less than the right side , which means that the given statement is false.
False
False
Step 9.3
Test a value on the interval to see if it makes the inequality true.
Tap for more steps...
Step 9.3.1
Choose a value on the interval and see if this value makes the original inequality true.
Step 9.3.2
Replace with in the original inequality.
Step 9.3.3
The left side is greater than the right side , which means that the given statement is always true.
True
True
Step 9.4
Compare the intervals to determine which ones satisfy the original inequality.
True
False
True
True
False
True
Step 10
The solution consists of all of the true intervals.
or
Step 11
The result can be shown in multiple forms.
Inequality Form:
Interval Notation:
Step 12