Algebra
Calculus
Trigonometry
Matrix
Question
Solve the inequality
Solve the inequality by testing the values in the interval
Solve the inequality by separating into cases
Solve for x
0<x<3
Alternative Form
x∈(0,3)
Evaluate
3x−x2>0
Rewrite the expression
3x−x2=0
Factor the expression
More Steps
Evaluate
3x−x2
Rewrite the expression
x×3−x×x
Factor out x from the expression
x(3−x)
x(3−x)=0
When the product of factors equals 0,at least one factor is 0
x=03−x=0
Solve the equation for x
More Steps
Evaluate
3−x=0
Move the constant to the right-hand side and change its sign
−x=0−3
Removing 0 doesn't change the value,so remove it from the expression
−x=−3
Change the signs on both sides of the equation
x=3
x=0x=3
Determine the test intervals using the critical values
x<00<x<3x>3
Choose a value form each interval
x1=−1x2=2x3=4
To determine if x<0 is the solution to the inequality,test if the chosen value x=−1 satisfies the initial inequality
More Steps
Evaluate
3(−1)−(−1)2>0
Simplify
More Steps
Evaluate
3(−1)−(−1)2
Evaluate the power
3(−1)−1
Simplify
−3−1
Subtract the numbers
−4
−4>0
Check the inequality
false
x<0 is not a solutionx2=2x3=4
To determine if 0<x<3 is the solution to the inequality,test if the chosen value x=2 satisfies the initial inequality
More Steps
Evaluate
3×2−22>0
Simplify
More Steps
Evaluate
3×2−22
Multiply the numbers
6−22
Evaluate the power
6−4
Subtract the numbers
2
2>0
Check the inequality
true
x<0 is not a solution0<x<3 is the solutionx3=4
To determine if x>3 is the solution to the inequality,test if the chosen value x=4 satisfies the initial inequality
More Steps
Evaluate
3×4−42>0
Simplify
More Steps
Evaluate
3×4−42
Multiply the numbers
12−42
Evaluate the power
12−16
Subtract the numbers
−4
−4>0
Check the inequality
false
x<0 is not a solution0<x<3 is the solutionx>3 is not a solution
Solution
0<x<3
Alternative Form
x∈(0,3)
Show Solution
