Question
Solve the inequality
Solve the inequality by testing the values in the interval
Solve the inequality by separating into cases
x∈(−∞,0)∪(0,234)
Evaluate
2x2−4x5>0
Rewrite the expression
2x2−4x5=0
Factor the expression
2x2(1−2x3)=0
Divide both sides
x2(1−2x3)=0
Separate the equation into 2 possible cases
x2=01−2x3=0
The only way a power can be 0 is when the base equals 0
x=01−2x3=0
Solve the equation
More Steps

Evaluate
1−2x3=0
Move the constant to the right-hand side and change its sign
−2x3=0−1
Removing 0 doesn't change the value,so remove it from the expression
−2x3=−1
Change the signs on both sides of the equation
2x3=1
Divide both sides
22x3=21
Divide the numbers
x3=21
Take the 3-th root on both sides of the equation
3x3=321
Calculate
x=321
Simplify the root
More Steps

Evaluate
321
To take a root of a fraction,take the root of the numerator and denominator separately
3231
Simplify the radical expression
321
Multiply by the Conjugate
32×322322
Simplify
32×32234
Multiply the numbers
234
x=234
x=0x=234
Determine the test intervals using the critical values
x<00<x<234x>234
Choose a value form each interval
x1=−1x2=434x3=2
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
2(−1)2−4(−1)5>0
Simplify
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Evaluate
2(−1)2−4(−1)5
Evaluate the power
2×1−4(−1)5
Any expression multiplied by 1 remains the same
2−4(−1)5
Multiply the terms
2−(−4)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
2+4
Add the numbers
6
6>0
Check the inequality
true
x<0 is the solutionx2=434x3=2
To determine if 0<x<234 is the solution to the inequality,test if the chosen value x=434 satisfies the initial inequality
More Steps

Evaluate
2(434)2−4(434)5>0
Simplify
More Steps

Evaluate
2(434)2−4(434)5
Multiply the terms
432−4(434)5
Multiply the terms
432−2532
Evaluate the power
432−3232
Reduce fractions to a common denominator
4×832×8−3232
Multiply the numbers
3232×8−3232
Write all numerators above the common denominator
3232×8−32
Use the commutative property to reorder the terms
32832−32
Subtract the numbers
32732
32732>0
Calculate
0.275608>0
Check the inequality
true
x<0 is the solution0<x<234 is the solutionx3=2
To determine if x>234 is the solution to the inequality,test if the chosen value x=2 satisfies the initial inequality
More Steps

Evaluate
2×22−4×25>0
Simplify
More Steps

Evaluate
2×22−4×25
Calculate the product
23−4×25
Multiply the terms
23−27
Evaluate the power
8−27
Evaluate the power
8−128
Subtract the numbers
−120
−120>0
Check the inequality
false
x<0 is the solution0<x<234 is the solutionx>234 is not a solution
Solution
x∈(−∞,0)∪(0,234)
Show Solution
