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]∪[6,+∞)
Evaluate
x2−3x×2≥0
Multiply the terms
x2−6x≥0
Rewrite the expression
x2−6x=0
Factor the expression
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Evaluate
x2−6x
Rewrite the expression
x×x−x×6
Factor out x from the expression
x(x−6)
x(x−6)=0
When the product of factors equals 0,at least one factor is 0
x=0x−6=0
Solve the equation for x
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Evaluate
x−6=0
Move the constant to the right-hand side and change its sign
x=0+6
Removing 0 doesn't change the value,so remove it from the expression
x=6
x=0x=6
Determine the test intervals using the critical values
x<00<x<6x>6
Choose a value form each interval
x1=−1x2=3x3=7
To determine if x<0 is the solution to the inequality,test if the chosen value x=−1 satisfies the initial inequality
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Evaluate
(−1)2−6(−1)≥0
Simplify
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Evaluate
(−1)2−6(−1)
Evaluate the power
1−6(−1)
Simplify
1−(−6)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
1+6
Add the numbers
7
7≥0
Check the inequality
true
x<0 is the solutionx2=3x3=7
To determine if 0<x<6 is the solution to the inequality,test if the chosen value x=3 satisfies the initial inequality
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Evaluate
32−6×3≥0
Simplify
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Evaluate
32−6×3
Multiply the numbers
32−18
Evaluate the power
9−18
Subtract the numbers
−9
−9≥0
Check the inequality
false
x<0 is the solution0<x<6 is not a solutionx3=7
To determine if x>6 is the solution to the inequality,test if the chosen value x=7 satisfies the initial inequality
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Evaluate
72−6×7≥0
Simplify
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Evaluate
72−6×7
Multiply the numbers
72−42
Evaluate the power
49−42
Subtract the numbers
7
7≥0
Check the inequality
true
x<0 is the solution0<x<6 is not a solutionx>6 is the solution
The original inequality is a nonstrict inequality,so include the critical value in the solution
x≤0 is the solutionx≥6 is the solution
Solution
x∈(−∞,0]∪[6,+∞)
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