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
x∈(−∞,−2)∪(0,2)
Evaluate
4x>x3
Move the expression to the left side
4x−x3>0
Rewrite the expression
4x−x3=0
Factor the expression
x(4−x2)=0
Separate the equation into 2 possible cases
x=04−x2=0
Solve the equation
More Steps
Evaluate
4−x2=0
Move the constant to the right-hand side and change its sign
−x2=0−4
Removing 0 doesn't change the value,so remove it from the expression
−x2=−4
Change the signs on both sides of the equation
x2=4
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±4
Simplify the expression
More Steps
Evaluate
4
Write the number in exponential form with the base of 2
22
Reduce the index of the radical and exponent with 2
2
x=±2
Separate the equation into 2 possible cases
x=2x=−2
x=0x=2x=−2
Determine the test intervals using the critical values
x<−2−2<x<00<x<2x>2
Choose a value form each interval
x1=−3x2=−1x3=1x4=3
To determine if x<−2 is the solution to the inequality,test if the chosen value x=−3 satisfies the initial inequality
More Steps
Evaluate
4(−3)>(−3)3
Multiply the numbers
More Steps
Evaluate
4(−3)
Multiplying or dividing an odd number of negative terms equals a negative
−4×3
Multiply the numbers
−12
−12>(−3)3
Calculate
−12>−33
Calculate
−12>−27
Check the inequality
true
x<−2 is the solutionx2=−1x3=1x4=3
To determine if −2<x<0 is the solution to the inequality,test if the chosen value x=−1 satisfies the initial inequality
More Steps
Evaluate
4(−1)>(−1)3
Simplify
−4>(−1)3
Calculate
−4>−1
Check the inequality
false
x<−2 is the solution−2<x<0 is not a solutionx3=1x4=3
To determine if 0<x<2 is the solution to the inequality,test if the chosen value x=1 satisfies the initial inequality
More Steps
Evaluate
4×1>13
Any expression multiplied by 1 remains the same
4>13
1 raised to any power equals to 1
4>1
Check the inequality
true
x<−2 is the solution−2<x<0 is not a solution0<x<2 is the solutionx4=3
To determine if x>2 is the solution to the inequality,test if the chosen value x=3 satisfies the initial inequality
More Steps
Evaluate
4×3>33
Multiply the numbers
12>33
Calculate
12>27
Check the inequality
false
x<−2 is the solution−2<x<0 is not a solution0<x<2 is the solutionx>2 is not a solution
Solution
x∈(−∞,−2)∪(0,2)
Show Solution
