Algebra
Calculus
Trigonometry
Matrix
Question
Solve the inequality
Solve the inequality by testing the values in the interval
Solve the inequality by separating into cases
Solve for x
x∈(−∞,0]∪[2,+∞)
Evaluate
2x≤x2
Move the expression to the left side
2x−x2≤0
Rewrite the expression
2x−x2=0
Factor the expression
More Steps
Evaluate
2x−x2
Rewrite the expression
x×2−x×x
Factor out x from the expression
x(2−x)
x(2−x)=0
When the product of factors equals 0,at least one factor is 0
x=02−x=0
Solve the equation for x
More Steps
Evaluate
2−x=0
Move the constant to the right-hand side and change its sign
−x=0−2
Removing 0 doesn't change the value,so remove it from the expression
−x=−2
Change the signs on both sides of the equation
x=2
x=0x=2
Determine the test intervals using the critical values
x<00<x<2x>2
Choose a value form each interval
x1=−1x2=1x3=3
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)≤(−1)2
Simplify
−2≤(−1)2
Evaluate the power
−2≤1
Check the inequality
true
x<0 is the solutionx2=1x3=3
To determine if 0<x<2 is the solution to the inequality,test if the chosen value x=1 satisfies the initial inequality
More Steps
Evaluate
2×1≤12
Any expression multiplied by 1 remains the same
2≤12
1 raised to any power equals to 1
2≤1
Check the inequality
false
x<0 is the solution0<x<2 is not a solutionx3=3
To determine if x>2 is the solution to the inequality,test if the chosen value x=3 satisfies the initial inequality
More Steps
Evaluate
2×3≤32
Multiply the numbers
6≤32
Calculate
6≤9
Check the inequality
true
x<0 is the solution0<x<2 is not a solutionx>2 is the solution
The original inequality is a nonstrict inequality,so include the critical value in the solution
x≤0 is the solutionx≥2 is the solution
Solution
x∈(−∞,0]∪[2,+∞)
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