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
−3<x<6
Alternative Form
x∈(−3,6)
Evaluate
x2−3x<18
Move the expression to the left side
x2−3x−18<0
Rewrite the expression
x2−3x−18=0
Factor the expression
More Steps
Evaluate
x2−3x−18
Rewrite the expression
x2+(3−6)x−18
Calculate
x2+3x−6x−18
Rewrite the expression
x×x+x×3−6x−6×3
Factor out x from the expression
x(x+3)−6x−6×3
Factor out −6 from the expression
x(x+3)−6(x+3)
Factor out x+3 from the expression
(x−6)(x+3)
(x−6)(x+3)=0
When the product of factors equals 0,at least one factor is 0
x−6=0x+3=0
Solve the equation for x
More Steps
Evaluate
x−6=0
Move the constant to the right-hand side and change its sign
x=0+6
Removing 0 doesn't change the value,so remove it from the expression
x=6
x=6x+3=0
Solve the equation for x
More Steps
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=6x=−3
Determine the test intervals using the critical values
x<−3−3<x<6x>6
Choose a value form each interval
x1=−4x2=2x3=7
To determine if x<−3 is the solution to the inequality,test if the chosen value x=−4 satisfies the initial inequality
More Steps
Evaluate
(−4)2−3(−4)<18
Simplify
More Steps
Evaluate
(−4)2−3(−4)
Multiply the numbers
(−4)2−(−12)
Rewrite the expression
42−(−12)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
42+12
Evaluate the power
16+12
Add the numbers
28
28<18
Check the inequality
false
x<−3 is not a solutionx2=2x3=7
To determine if −3<x<6 is the solution to the inequality,test if the chosen value x=2 satisfies the initial inequality
More Steps
Evaluate
22−3×2<18
Simplify
More Steps
Evaluate
22−3×2
Multiply the numbers
22−6
Evaluate the power
4−6
Subtract the numbers
−2
−2<18
Check the inequality
true
x<−3 is not a solution−3<x<6 is the solutionx3=7
To determine if x>6 is the solution to the inequality,test if the chosen value x=7 satisfies the initial inequality
More Steps
Evaluate
72−3×7<18
Simplify
More Steps
Evaluate
72−3×7
Multiply the numbers
72−21
Evaluate the power
49−21
Subtract the numbers
28
28<18
Check the inequality
false
x<−3 is not a solution−3<x<6 is the solutionx>6 is not a solution
Solution
−3<x<6
Alternative Form
x∈(−3,6)
Show Solution
