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∈(−∞,3)∪(6,+∞)
Evaluate
(x−3)(x−6)>0
Rewrite the expression
(x−3)(x−6)=0
Separate the equation into 2 possible cases
x−3=0x−6=0
Solve the equation
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Evaluate
x−3=0
Move the constant to the right-hand side and change its sign
x=0+3
Removing 0 doesn't change the value,so remove it from the expression
x=3
x=3x−6=0
Solve the equation
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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=3x=6
Determine the test intervals using the critical values
x<33<x<6x>6
Choose a value form each interval
x1=2x2=5x3=7
To determine if x<3 is the solution to the inequality,test if the chosen value x=2 satisfies the initial inequality
More Steps
Evaluate
(2−3)(2−6)>0
Simplify
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Evaluate
(2−3)(2−6)
Subtract the numbers
(−1)(2−6)
Remove the parentheses
−(2−6)
Subtract the numbers
−(−4)
When there is - in front of an expression in parentheses change the sign of each term of the expression and remove the parentheses
4
4>0
Check the inequality
true
x<3 is the solutionx2=5x3=7
To determine if 3<x<6 is the solution to the inequality,test if the chosen value x=5 satisfies the initial inequality
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Evaluate
(5−3)(5−6)>0
Simplify
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Evaluate
(5−3)(5−6)
Subtract the numbers
2(5−6)
Subtract the numbers
2(−1)
Simplify
−2
−2>0
Check the inequality
false
x<3 is the solution3<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
More Steps
Evaluate
(7−3)(7−6)>0
Simplify
More Steps
Evaluate
(7−3)(7−6)
Subtract the numbers
4(7−6)
Subtract the numbers
4×1
Any expression multiplied by 1 remains the same
4
4>0
Check the inequality
true
x<3 is the solution3<x<6 is not a solutionx>6 is the solution
Solution
x∈(−∞,3)∪(6,+∞)
Show Solution
