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
x∈(−1,0)∪(0,3)
Evaluate
(x2−2x−3)(−x2−3x4)>0
Rewrite the expression
(x2−2x−3)(−x2−3x4)=0
Separate the equation into 2 possible cases
x2−2x−3=0−x2−3x4=0
Solve the equation
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Evaluate
x2−2x−3=0
Factor the expression
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Evaluate
x2−2x−3
Rewrite the expression
x2+(1−3)x−3
Calculate
x2+x−3x−3
Rewrite the expression
x×x+x−3x−3
Factor out x from the expression
x(x+1)−3x−3
Factor out −3 from the expression
x(x+1)−3(x+1)
Factor out x+1 from the expression
(x−3)(x+1)
(x−3)(x+1)=0
When the product of factors equals 0,at least one factor is 0
x−3=0x+1=0
Solve the equation for x
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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+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=3x=−1
x=3x=−1−x2−3x4=0
Solve the equation
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Evaluate
−x2−3x4=0
The statement is true only the each term equals to 0
{−x2=0−3x4=0
Calculate
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Evaluate
−x2=0
Change the signs on both sides of the equation
x2=0
The only way a power can be 0 is when the base equals 0
x=0
{x=0−3x4=0
Calculate
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Evaluate
−3x4=0
Change the signs on both sides of the equation
3x4=0
Rewrite the expression
x4=0
The only way a power can be 0 is when the base equals 0
x=0
{x=0x=0
Find the intersection
x=0
x=3x=−1x=0
Determine the test intervals using the critical values
x<−1−1<x<00<x<3x>3
Choose a value form each interval
x1=−2x2=−21x3=2x4=4
To determine if x<−1 is the solution to the inequality,test if the chosen value x=−2 satisfies the initial inequality
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Evaluate
((−2)2−2(−2)−3)(−(−2)2−3(−2)4)>0
Simplify
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Evaluate
((−2)2−2(−2)−3)(−(−2)2−3(−2)4)
Multiply the numbers
((−2)2+4−3)(−(−2)2−3(−2)4)
Calculate the sum or difference
5(−(−2)2−3(−2)4)
Multiply the terms
5(−(−2)2−48)
Subtract the numbers
5(−52)
Multiplying or dividing an odd number of negative terms equals a negative
−5×52
Multiply the numbers
−260
−260>0
Check the inequality
false
x<−1 is not a solutionx2=−21x3=2x4=4
To determine if −1<x<0 is the solution to the inequality,test if the chosen value x=−21 satisfies the initial inequality
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Evaluate
((−21)2−2(−21)−3)(−(−21)2−3(−21)4)>0
Simplify
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Evaluate
((−21)2−2(−21)−3)(−(−21)2−3(−21)4)
Multiply the numbers
((−21)2+1−3)(−(−21)2−3(−21)4)
Calculate the sum or difference
(−47)(−(−21)2−3(−21)4)
Remove the parentheses
−47(−(−21)2−3(−21)4)
Multiply the terms
−47(−(−21)2−163)
Subtract the numbers
−47(−167)
Multiplying or dividing an even number of negative terms equals a positive
47×167
To multiply the fractions,multiply the numerators and denominators separately
4×167×7
Multiply the numbers
4×1649
Multiply the numbers
6449
6449>0
Calculate
0.765625>0
Check the inequality
true
x<−1 is not a solution−1<x<0 is the solutionx3=2x4=4
To determine if 0<x<3 is the solution to the inequality,test if the chosen value x=2 satisfies the initial inequality
More Steps
Evaluate
(22−2×2−3)(−22−3×24)>0
Simplify
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Evaluate
(22−2×2−3)(−22−3×24)
Multiply the numbers
(22−4−3)(−22−3×24)
Apply the inverse property of addition
(−3)(−22−3×24)
Remove the parentheses
−3(−22−3×24)
Multiply the terms
−3(−22−48)
Subtract the numbers
−3(−52)
Multiplying or dividing an even number of negative terms equals a positive
3×52
Multiply the numbers
156
156>0
Check the inequality
true
x<−1 is not a solution−1<x<0 is the solution0<x<3 is the solutionx4=4
To determine if x>3 is the solution to the inequality,test if the chosen value x=4 satisfies the initial inequality
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Evaluate
(42−2×4−3)(−42−3×44)>0
Simplify
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Evaluate
(42−2×4−3)(−42−3×44)
Multiply the numbers
(42−8−3)(−42−3×44)
Subtract the numbers
5(−42−3×44)
Multiply the terms
5(−42−768)
Subtract the numbers
5(−784)
Multiplying or dividing an odd number of negative terms equals a negative
−5×784
Multiply the numbers
−3920
−3920>0
Check the inequality
false
x<−1 is not a solution−1<x<0 is the solution0<x<3 is the solutionx>3 is not a solution
Solution
x∈(−1,0)∪(0,3)
Show Solution
