Algebra
Calculus
Trigonometry
Matrix
Question
Solve the system of inequalities
x∈(−∞,0)∪[1,+∞)
Evaluate
{x2−x31≥0x2−5x2≤0
Find the domain
More Steps
Evaluate
x3=0
The only way a power can not be 0 is when the base not equals 0
x=0
{x2−x31≥0x2−5x2≤0,x=0
Solve the inequality
More Steps
Evaluate
x2−x31≥0
Convert the expressions
x3x5−1≥0
Separate the inequality into 2 possible cases
{x5−1≥0x3>0{x5−1≤0x3<0
Solve the inequality
More Steps
Evaluate
x5−1≥0
Move the constant to the right side
x5≥1
Take the 5-th root on both sides of the equation
5x5≥51
Calculate
x≥51
Simplify the root
x≥1
{x≥1x3>0{x5−1≤0x3<0
The only way a base raised to an odd power can be greater than 0 is if the base is greater than 0
{x≥1x>0{x5−1≤0x3<0
Solve the inequality
More Steps
Evaluate
x5−1≤0
Move the constant to the right side
x5≤1
Take the 5-th root on both sides of the equation
5x5≤51
Calculate
x≤51
Simplify the root
x≤1
{x≥1x>0{x≤1x3<0
The only way a base raised to an odd power can be less than 0 is if the base is less than 0
{x≥1x>0{x≤1x<0
Find the intersection
x≥1{x≤1x<0
Find the intersection
x≥1x<0
Find the union
x∈(−∞,0)∪[1,+∞)
{x∈(−∞,0)∪[1,+∞)x2−5x2≤0
Solve the inequality
More Steps
Evaluate
x2−5x2≤0
Subtract the terms
More Steps
Evaluate
x2−5x2
Collect like terms by calculating the sum or difference of their coefficients
(1−5)x2
Subtract the numbers
−4x2
−4x2≤0
Since the left-hand side is always negative or 0,and the right-hand side is always 0,the statement is true for any value of x
x∈R
{x∈(−∞,0)∪[1,+∞)x∈R
Find the intersection
x∈(−∞,0)∪[1,+∞)
Check if the solution is in the defined range
x∈(−∞,0)∪[1,+∞),x=0
Solution
x∈(−∞,0)∪[1,+∞)
Show Solution
