Algebra
Calculus
Trigonometry
Matrix
Question
Solve the inequality
x>833+1
Alternative Form
x∈(833+1,+∞)
Evaluate
x−3<(x)2×4x−5
Find the domain
x−3<(x)2×4x−5,x≥0
Multiply the terms
More Steps
Evaluate
(x)2×4x
Multiply the terms
More Steps
Evaluate
(x)2×4
Rewrite the expression
x×4
Use the commutative property to reorder the terms
4x
4x×x
Multiply the terms
4x2
x−3<4x2−5
Move the expression to the left side
x−3−(4x2−5)<0
Subtract the terms
More Steps
Evaluate
x−3−(4x2−5)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
x−3−4x2+5
Add the numbers
x+2−4x2
x+2−4x2<0
Move the constant to the right side
x−4x2<0−2
Add the terms
x−4x2<−2
Evaluate
x2−41x>21
Add the same value to both sides
x2−41x+641>21+641
Evaluate
x2−41x+641>6433
Evaluate
(x−81)2>6433
Take the 2-th root on both sides of the inequality
(x−81)2>6433
Calculate
x−81>833
Separate the inequality into 2 possible cases
x−81>833x−81<−833
Calculate
More Steps
Evaluate
x−81>833
Move the constant to the right side
x>833+81
Write all numerators above the common denominator
x>833+1
x>833+1x−81<−833
Calculate
More Steps
Evaluate
x−81<−833
Move the constant to the right side
x<−833+81
Write all numerators above the common denominator
x<8−33+1
x>833+1x<8−33+1
Find the union
x∈(−∞,8−33+1)∪(833+1,+∞)
Check if the solution is in the defined range
x∈(−∞,8−33+1)∪(833+1,+∞),x≥0
Solution
x>833+1
Alternative Form
x∈(833+1,+∞)
Show Solution
