Algebra
Calculus
Trigonometry
Matrix
Question
Solve the inequality
x∈R
Alternative Form
All real solution
Evaluate
−3x2∣x×1∣−x<1
Simplify
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Evaluate
−3x2∣x×1∣−x
Any expression multiplied by 1 remains the same
−3x2∣x∣−x
Calculate the absolute value
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Calculate
3x2
Rewrite the expression
3x2
Simplify
3x2
−3x2∣x∣−x
−3x2∣x∣−x<1
Separate the inequality into 2 possible cases
−3x2×x−x<1,x≥0−3x2(−x)−x<1,x<0
Evaluate
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Evaluate
−3x2×x−x<1
Simplify the expression
−3x3−x<1
Move the expression to the left side
−3x3−x−1<0
Rewrite the expression
−3x3−x−1=0
Factor the expression
−(3x3+x+1)=0
Divide both sides
3x3+x+1=0
Calculate
x≈−0.536565
Determine the test intervals using the critical values
x<−0.536565x>−0.536565
Choose a value form each interval
x1=−2x2=0
To determine if x<−0.536565 is the solution to the inequality,test if the chosen value x=−2 satisfies the initial inequality
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Evaluate
−3(−2)3−(−2)−1<0
Simplify
25<0
Check the inequality
false
x<−0.536565 is not a solutionx2=0
To determine if x>−0.536565 is the solution to the inequality,test if the chosen value x=0 satisfies the initial inequality
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Evaluate
−3×03−0−1<0
Simplify
−1<0
Check the inequality
true
x<−0.536565 is not a solutionx>−0.536565 is the solution
The original inequality is a strict inequality,so does not include the critical value ,the final solution is x>−0.536565
x>−0.536565
x>−0.536565,x≥0−3x2(−x)−x<1,x<0
Evaluate
More Steps
Evaluate
−3x2(−x)−x<1
Simplify the expression
3x3−x<1
Move the expression to the left side
3x3−x−1<0
Rewrite the expression
3x3−x−1=0
Find the critical values by solving the corresponding equation
x≈0.851383
Determine the test intervals using the critical values
x<0.851383x>0.851383
Choose a value form each interval
x1=0x2=2
To determine if x<0.851383 is the solution to the inequality,test if the chosen value x=0 satisfies the initial inequality
More Steps
Evaluate
3×03−0−1<0
Simplify
−1<0
Check the inequality
true
x<0.851383 is the solutionx2=2
To determine if x>0.851383 is the solution to the inequality,test if the chosen value x=2 satisfies the initial inequality
More Steps
Evaluate
3×23−2−1<0
Simplify
21<0
Check the inequality
false
x<0.851383 is the solutionx>0.851383 is not a solution
The original inequality is a strict inequality,so does not include the critical value ,the final solution is x<0.851383
x<0.851383
x>−0.536565,x≥0x<0.851383,x<0
Find the intersection
x≥0x<0.851383,x<0
Find the intersection
x≥0x<0
Solution
x∈R
Alternative Form
All real solution
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