Algebra
Calculus
Trigonometry
Matrix
Question
Solve the inequality
x>0.64679
Alternative Form
x∈(0.64679,+∞)
Evaluate
(x−1)×−1(x−2)2−x<0
Simplify
More Steps
Evaluate
(x−1)×−1(x−2)2−x
Divide the terms
(x−1)(−(x−2)2)−x
Multiply the terms
−(x−1)(x−2)2−x
Rewrite the expression
(−x+1)(x−2)2−x
(−x+1)(x−2)2−x<0
Rearrange the terms
−x3+5x2−9x+4<0
Rewrite the expression
−x3+5x2−9x+4=0
Find the critical values by solving the corresponding equation
x≈0.64679
Determine the test intervals using the critical values
x<0.64679x>0.64679
Choose a value form each interval
x1=0x2=2
To determine if x<0.64679 is the solution to the inequality,test if the chosen value x=0 satisfies the initial inequality
More Steps
Evaluate
(0+1)(0−2)2−0<0
Simplify
More Steps
Evaluate
(0+1)(0−2)2−0
Removing 0 doesn't change the value,so remove it from the expression
1×(0−2)2−0
Removing 0 doesn't change the value,so remove it from the expression
1×(−2)2−0
Multiply the terms
22−0
Removing 0 doesn't change the value,so remove it from the expression
22
22<0
Calculate
4<0
Check the inequality
false
x<0.64679 is not a solutionx2=2
To determine if x>0.64679 is the solution to the inequality,test if the chosen value x=2 satisfies the initial inequality
More Steps
Evaluate
(−2+1)(2−2)2−2<0
Simplify
More Steps
Evaluate
(−2+1)(2−2)2−2
Add the numbers
(−1)(2−2)2−2
Remove the parentheses
−(2−2)2−2
Subtract the numbers
−02−2
Calculate
−1×0−2
Any expression multiplied by 0 equals 0
0−2
Removing 0 doesn't change the value,so remove it from the expression
−2
−2<0
Check the inequality
true
x<0.64679 is not a solutionx>0.64679 is the solution
Solution
x>0.64679
Alternative Form
x∈(0.64679,+∞)
Show Solution
