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∈(−∞,2)∪(5,+∞)
Evaluate
x2−7x+10>0
Rewrite the expression
x2−7x+10=0
Factor the expression
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Evaluate
x2−7x+10
Rewrite the expression
x2+(−2−5)x+10
Calculate
x2−2x−5x+10
Rewrite the expression
x×x−x×2−5x+5×2
Factor out x from the expression
x(x−2)−5x+5×2
Factor out −5 from the expression
x(x−2)−5(x−2)
Factor out x−2 from the expression
(x−5)(x−2)
(x−5)(x−2)=0
When the product of factors equals 0,at least one factor is 0
x−5=0x−2=0
Solve the equation for x
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Evaluate
x−5=0
Move the constant to the right-hand side and change its sign
x=0+5
Removing 0 doesn't change the value,so remove it from the expression
x=5
x=5x−2=0
Solve the equation for x
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Evaluate
x−2=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
x=5x=2
Determine the test intervals using the critical values
x<22<x<5x>5
Choose a value form each interval
x1=1x2=4x3=6
To determine if x<2 is the solution to the inequality,test if the chosen value x=1 satisfies the initial inequality
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Evaluate
12−7×1+10>0
Simplify
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Evaluate
12−7×1+10
1 raised to any power equals to 1
1−7×1+10
Any expression multiplied by 1 remains the same
1−7+10
Calculate the sum or difference
4
4>0
Check the inequality
true
x<2 is the solutionx2=4x3=6
To determine if 2<x<5 is the solution to the inequality,test if the chosen value x=4 satisfies the initial inequality
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Evaluate
42−7×4+10>0
Simplify
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Evaluate
42−7×4+10
Multiply the numbers
42−28+10
Evaluate the power
16−28+10
Calculate the sum or difference
−2
−2>0
Check the inequality
false
x<2 is the solution2<x<5 is not a solutionx3=6
To determine if x>5 is the solution to the inequality,test if the chosen value x=6 satisfies the initial inequality
More Steps

Evaluate
62−7×6+10>0
Simplify
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Evaluate
62−7×6+10
Multiply the numbers
62−42+10
Evaluate the power
36−42+10
Calculate the sum or difference
4
4>0
Check the inequality
true
x<2 is the solution2<x<5 is not a solutionx>5 is the solution
Solution
x∈(−∞,2)∪(5,+∞)
Show Solution
