Question
Solve the inequality
Solve the inequality by testing the values in the interval
Solve for x
x≤−3336
Alternative Form
x∈(−∞,−3336]
Evaluate
−x3×3≥4
Use the commutative property to reorder the terms
−3x3≥4
Move the expression to the left side
−3x3−4≥0
Rewrite the expression
−3x3−4=0
Move the constant to the right-hand side and change its sign
−3x3=0+4
Removing 0 doesn't change the value,so remove it from the expression
−3x3=4
Change the signs on both sides of the equation
3x3=−4
Divide both sides
33x3=3−4
Divide the numbers
x3=3−4
Use b−a=−ba=−ba to rewrite the fraction
x3=−34
Take the 3-th root on both sides of the equation
3x3=3−34
Calculate
x=3−34
Simplify the root
More Steps

Evaluate
3−34
An odd root of a negative radicand is always a negative
−334
To take a root of a fraction,take the root of the numerator and denominator separately
−3334
Multiply by the Conjugate
33×332−34×332
Simplify
33×332−34×39
Multiply the numbers
More Steps

Evaluate
−34×39
The product of roots with the same index is equal to the root of the product
−34×9
Calculate the product
−336
33×332−336
Multiply the numbers
More Steps

Evaluate
33×332
The product of roots with the same index is equal to the root of the product
33×32
Calculate the product
333
Reduce the index of the radical and exponent with 3
3
3−336
Calculate
−3336
x=−3336
Determine the test intervals using the critical values
x<−3336x>−3336
Choose a value form each interval
x1=−2x2=0
To determine if x<−3336 is the solution to the inequality,test if the chosen value x=−2 satisfies the initial inequality
More Steps

Evaluate
−3(−2)3≥4
Multiply the terms
More Steps

Evaluate
−3(−2)3
Evaluate the power
−3(−8)
Multiply the numbers
24
24≥4
Check the inequality
true
x<−3336 is the solutionx2=0
To determine if x>−3336 is the solution to the inequality,test if the chosen value x=0 satisfies the initial inequality
More Steps

Evaluate
−3×03≥4
Simplify
More Steps

Evaluate
−3×03
Calculate
−3×0
Any expression multiplied by 0 equals 0
0
0≥4
Check the inequality
false
x<−3336 is the solutionx>−3336 is not a solution
The original inequality is a nonstrict inequality,so include the critical value in the solution
x≤−3336 is the solution
Solution
x≤−3336
Alternative Form
x∈(−∞,−3336]
Show Solution
