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∈(−∞,−1)∪(15,+∞)
Evaluate
x2−14x>15
Move the expression to the left side
x2−14x−15>0
Rewrite the expression
x2−14x−15=0
Factor the expression
More Steps
Evaluate
x2−14x−15
Rewrite the expression
x2+(1−15)x−15
Calculate
x2+x−15x−15
Rewrite the expression
x×x+x−15x−15
Factor out x from the expression
x(x+1)−15x−15
Factor out −15 from the expression
x(x+1)−15(x+1)
Factor out x+1 from the expression
(x−15)(x+1)
(x−15)(x+1)=0
When the product of factors equals 0,at least one factor is 0
x−15=0x+1=0
Solve the equation for x
More Steps
Evaluate
x−15=0
Move the constant to the right-hand side and change its sign
x=0+15
Removing 0 doesn't change the value,so remove it from the expression
x=15
x=15x+1=0
Solve the equation for x
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Evaluate
x+1=0
Move the constant to the right-hand side and change its sign
x=0−1
Removing 0 doesn't change the value,so remove it from the expression
x=−1
x=15x=−1
Determine the test intervals using the critical values
x<−1−1<x<15x>15
Choose a value form each interval
x1=−2x2=7x3=16
To determine if x<−1 is the solution to the inequality,test if the chosen value x=−2 satisfies the initial inequality
More Steps
Evaluate
(−2)2−14(−2)>15
Simplify
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Evaluate
(−2)2−14(−2)
Multiply the numbers
(−2)2−(−28)
Rewrite the expression
22−(−28)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
22+28
Evaluate the power
4+28
Add the numbers
32
32>15
Check the inequality
true
x<−1 is the solutionx2=7x3=16
To determine if −1<x<15 is the solution to the inequality,test if the chosen value x=7 satisfies the initial inequality
More Steps
Evaluate
72−14×7>15
Simplify
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Evaluate
72−14×7
Multiply the numbers
72−98
Evaluate the power
49−98
Subtract the numbers
−49
−49>15
Check the inequality
false
x<−1 is the solution−1<x<15 is not a solutionx3=16
To determine if x>15 is the solution to the inequality,test if the chosen value x=16 satisfies the initial inequality
More Steps
Evaluate
162−14×16>15
Simplify
More Steps
Evaluate
162−14×16
Multiply the numbers
162−224
Evaluate the power
256−224
Subtract the numbers
32
32>15
Check the inequality
true
x<−1 is the solution−1<x<15 is not a solutionx>15 is the solution
Solution
x∈(−∞,−1)∪(15,+∞)
Show Solution
