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
−3<s<0
Alternative Form
s∈(−3,0)
Evaluate
−9>s3−8
Find the domain
−9>s3−8,s=0
Move the expression to the left side
−9−(s3−8)>0
Subtract the terms
More Steps
Evaluate
−9−(s3−8)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
−9−s3+8
Add the numbers
−1−s3
Reduce fractions to a common denominator
−ss−s3
Write all numerators above the common denominator
s−s−3
Use b−a=−ba=−ba to rewrite the fraction
−ss+3
−ss+3>0
Change the signs on both sides of the inequality and flip the inequality sign
ss+3<0
Set the numerator and denominator of ss+3 equal to 0 to find the values of s where sign changes may occur
s+3=0s=0
Calculate
More Steps
Evaluate
s+3=0
Move the constant to the right-hand side and change its sign
s=0−3
Removing 0 doesn't change the value,so remove it from the expression
s=−3
s=−3s=0
Determine the test intervals using the critical values
s<−3−3<s<0s>0
Choose a value form each interval
s1=−4s2=−2s3=1
To determine if s<−3 is the solution to the inequality,test if the chosen value s=−4 satisfies the initial inequality
More Steps
Evaluate
−9>−43−8
Simplify
More Steps
Evaluate
−43−8
Use b−a=−ba=−ba to rewrite the fraction
−43−8
Reduce fractions to a common denominator
−43−48×4
Write all numerators above the common denominator
4−3−8×4
Multiply the numbers
4−3−32
Subtract the numbers
4−35
Use b−a=−ba=−ba to rewrite the fraction
−435
−9>−435
Calculate
−9>−8.75
Check the inequality
false
s<−3 is not a solutions2=−2s3=1
To determine if −3<s<0 is the solution to the inequality,test if the chosen value s=−2 satisfies the initial inequality
More Steps
Evaluate
−9>−23−8
Simplify
More Steps
Evaluate
−23−8
Use b−a=−ba=−ba to rewrite the fraction
−23−8
Reduce fractions to a common denominator
−23−28×2
Write all numerators above the common denominator
2−3−8×2
Multiply the numbers
2−3−16
Subtract the numbers
2−19
Use b−a=−ba=−ba to rewrite the fraction
−219
−9>−219
Calculate
−9>−9.5
Check the inequality
true
s<−3 is not a solution−3<s<0 is the solutions3=1
To determine if s>0 is the solution to the inequality,test if the chosen value s=1 satisfies the initial inequality
More Steps
Evaluate
−9>13−8
Simplify
More Steps
Evaluate
13−8
Divide the terms
3−8
Subtract the numbers
−5
−9>−5
Check the inequality
false
s<−3 is not a solution−3<s<0 is the solutions>0 is not a solution
The original inequality is a strict inequality,so does not include the critical value ,the final solution is −3<s<0
−3<s<0
Check if the solution is in the defined range
−3<s<0,s=0
Solution
−3<s<0
Alternative Form
s∈(−3,0)
Show Solution
