Question
Solve the inequality
Solve the inequality by testing the values in the interval
Solve the inequality by separating into cases
x<−2
Alternative Form
x∈(−∞,−2)
Evaluate
2x3<5x−6
Move the expression to the left side
2x3−(5x−6)<0
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
2x3−5x+6<0
Rewrite the expression
2x3−5x+6=0
Factor the expression
(x+2)(2x2−4x+3)=0
Separate the equation into 2 possible cases
x+2=02x2−4x+3=0
Solve the equation
More Steps

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=−22x2−4x+3=0
Solve the equation
More Steps

Evaluate
2x2−4x+3=0
Add or subtract both sides
2x2−4x=−3
Divide both sides
22x2−4x=2−3
Evaluate
x2−2x=−23
Add the same value to both sides
x2−2x+1=−23+1
Simplify the expression
(x−1)2=−21
Since the left-hand side is always positive or 0,and the right-hand side is always negative,the statement is false for any value of x
x∈/R
x=−2x∈/R
Find the union
x=−2
Determine the test intervals using the critical values
x<−2x>−2
Choose a value form each interval
x1=−3x2=−1
To determine if x<−2 is the solution to the inequality,test if the chosen value x=−3 satisfies the initial inequality
More Steps

Evaluate
2(−3)3<5(−3)−6
Multiply the terms
More Steps

Evaluate
2(−3)3
Evaluate the power
2(−27)
Multiply the numbers
−54
−54<5(−3)−6
Simplify
More Steps

Evaluate
5(−3)−6
Multiply the numbers
−15−6
Subtract the numbers
−21
−54<−21
Check the inequality
true
x<−2 is the solutionx2=−1
To determine if x>−2 is the solution to the inequality,test if the chosen value x=−1 satisfies the initial inequality
More Steps

Evaluate
2(−1)3<5(−1)−6
Multiply the terms
More Steps

Evaluate
2(−1)3
Evaluate the power
2(−1)
Multiply the numbers
−2
−2<5(−1)−6
Simplify
More Steps

Evaluate
5(−1)−6
Simplify
−5−6
Subtract the numbers
−11
−2<−11
Check the inequality
false
x<−2 is the solutionx>−2 is not a solution
Solution
x<−2
Alternative Form
x∈(−∞,−2)
Show Solution
