Question
Solve the inequality
Solve the inequality by testing the values in the interval
Solve the inequality by separating into cases
Solve for x
−21<x<4
Alternative Form
x∈(−21,4)
Evaluate
x2−2<27x
Move the expression to the left side
x2−2−27x<0
Rewrite the expression
x2−2−27x=0
Factor the expression
More Steps

Evaluate
x2−2−27x
Evaluate
x2−27x−2
Rewrite the expression
21×2x2−21×7x−21×4
Factor out 21 from the expression
21(2x2−7x−4)
Factor the expression
More Steps

Evaluate
2x2−7x−4
Rewrite the expression
2x2+(1−8)x−4
Calculate
2x2+x−8x−4
Rewrite the expression
x×2x+x−4×2x−4
Factor out x from the expression
x(2x+1)−4×2x−4
Factor out −4 from the expression
x(2x+1)−4(2x+1)
Factor out 2x+1 from the expression
(x−4)(2x+1)
21(x−4)(2x+1)
21(x−4)(2x+1)=0
Divide the terms
(x−4)(2x+1)=0
When the product of factors equals 0,at least one factor is 0
x−4=02x+1=0
Solve the equation for x
More Steps

Evaluate
x−4=0
Move the constant to the right-hand side and change its sign
x=0+4
Removing 0 doesn't change the value,so remove it from the expression
x=4
x=42x+1=0
Solve the equation for x
More Steps

Evaluate
2x+1=0
Move the constant to the right-hand side and change its sign
2x=0−1
Removing 0 doesn't change the value,so remove it from the expression
2x=−1
Divide both sides
22x=2−1
Divide the numbers
x=2−1
Use b−a=−ba=−ba to rewrite the fraction
x=−21
x=4x=−21
Determine the test intervals using the critical values
x<−21−21<x<4x>4
Choose a value form each interval
x1=−2x2=2x3=5
To determine if x<−21 is the solution to the inequality,test if the chosen value x=−2 satisfies the initial inequality
More Steps

Evaluate
(−2)2−2<27(−2)
Subtract the numbers
More Steps

Evaluate
(−2)2−2
Simplify
22−2
Evaluate the power
4−2
Subtract the numbers
2
2<27(−2)
Multiply the numbers
More Steps

Evaluate
27(−2)
Multiplying or dividing an odd number of negative terms equals a negative
−27×2
Reduce the numbers
−7×1
Simplify
−7
2<−7
Check the inequality
false
x<−21 is not a solutionx2=2x3=5
To determine if −21<x<4 is the solution to the inequality,test if the chosen value x=2 satisfies the initial inequality
More Steps

Evaluate
22−2<27×2
Subtract the numbers
More Steps

Evaluate
22−2
Evaluate the power
4−2
Subtract the numbers
2
2<27×2
Multiply the numbers
More Steps

Evaluate
27×2
Reduce the numbers
7×1
Simplify
7
2<7
Check the inequality
true
x<−21 is not a solution−21<x<4 is the solutionx3=5
To determine if x>4 is the solution to the inequality,test if the chosen value x=5 satisfies the initial inequality
More Steps

Evaluate
52−2<27×5
Subtract the numbers
More Steps

Evaluate
52−2
Evaluate the power
25−2
Subtract the numbers
23
23<27×5
Multiply the numbers
More Steps

Evaluate
27×5
Multiply the numbers
27×5
Multiply the numbers
235
23<235
Calculate
23<17.5
Check the inequality
false
x<−21 is not a solution−21<x<4 is the solutionx>4 is not a solution
Solution
−21<x<4
Alternative Form
x∈(−21,4)
Show Solution
