Algebra
Calculus
Trigonometry
Matrix
Question
x2−4x≤32
Solve the inequality
Solve the inequality by testing the values in the interval
Solve the inequality by separating into cases
Solve for x
−4≤x≤8
Alternative Form
x∈[−4,8]
Evaluate
x2−4x≤32
Move the expression to the left side
x2−4x−32≤0
Rewrite the expression
x2−4x−32=0
Factor the expression
More Steps
Evaluate
x2−4x−32
Rewrite the expression
x2+(4−8)x−32
Calculate
x2+4x−8x−32
Rewrite the expression
x×x+x×4−8x−8×4
Factor out x from the expression
x(x+4)−8x−8×4
Factor out −8 from the expression
x(x+4)−8(x+4)
Factor out x+4 from the expression
(x−8)(x+4)
(x−8)(x+4)=0
When the product of factors equals 0,at least one factor is 0
x−8=0x+4=0
Solve the equation for x
More Steps
Evaluate
x−8=0
Move the constant to the right-hand side and change its sign
x=0+8
Removing 0 doesn't change the value,so remove it from the expression
x=8
x=8x+4=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=8x=−4
Determine the test intervals using the critical values
x<−4−4<x<8x>8
Choose a value form each interval
x1=−5x2=2x3=9
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
(−5)2−4(−5)≤32
Simplify
More Steps
Evaluate
(−5)2−4(−5)
Multiply the numbers
(−5)2−(−20)
Rewrite the expression
52−(−20)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
52+20
Evaluate the power
25+20
Add the numbers
45
45≤32
Check the inequality
false
x<−4 is not a solutionx2=2x3=9
To determine if −4<x<8 is the solution to the inequality,test if the chosen value x=2 satisfies the initial inequality
More Steps
Evaluate
22−4×2≤32
Simplify
More Steps
Evaluate
22−4×2
Multiply the numbers
22−8
Evaluate the power
4−8
Subtract the numbers
−4
−4≤32
Check the inequality
true
x<−4 is not a solution−4<x<8 is the solutionx3=9
To determine if x>8 is the solution to the inequality,test if the chosen value x=9 satisfies the initial inequality
More Steps
Evaluate
92−4×9≤32
Simplify
More Steps
Evaluate
92−4×9
Multiply the numbers
92−36
Evaluate the power
81−36
Subtract the numbers
45
45≤32
Check the inequality
false
x<−4 is not a solution−4<x<8 is the solutionx>8 is not a solution
The original inequality is a nonstrict inequality,so include the critical value in the solution
−4≤x≤8 is the solution
Solution
−4≤x≤8
Alternative Form
x∈[−4,8]
Show Solution
