Question
Solve the inequality
Solve for x
x>53100
Alternative Form
x∈(53100,+∞)
Evaluate
0x2×25x−2<5
Find the domain
More Steps

Evaluate
x2×25x−2>0
Multiply
More Steps

Evaluate
x2×25x
Multiply the terms with the same base by adding their exponents
x2+1×25
Add the numbers
x3×25
Use the commutative property to reorder the terms
25x3
25x3−2>0
Move the constant to the right side
25x3>2
Multiply by the reciprocal
25x3×52>2×52
Multiply
x3>2×52
Multiply
More Steps

Evaluate
2×52
Multiply the numbers
52×2
Multiply the numbers
54
x3>54
Take the 3-th root on both sides of the equation
3x3>354
Calculate
x>354
Simplify the root
More Steps

Evaluate
354
To take a root of a fraction,take the root of the numerator and denominator separately
3534
Multiply by the Conjugate
35×35234×352
Simplify
35×35234×325
Multiply the numbers
35×3523100
Multiply the numbers
53100
x>53100
0x2×25x−2<5,x>53100
Simplify
More Steps

Evaluate
0x2×25x−2
Multiply
More Steps

Multiply the terms
x2×25x
Multiply the terms with the same base by adding their exponents
x2+1×25
Add the numbers
x3×25
Use the commutative property to reorder the terms
25x3
025x3−2
Calculate
0
0<5
Calculate
0<2.236068
The statement is true for any value of x
x∈R
Check if the solution is in the defined range
x∈R,x>53100
Solution
x>53100
Alternative Form
x∈(53100,+∞)
Show Solution