Algebra
Calculus
Trigonometry
Matrix
Question
Solve the inequality
−1.172988<a<0.857114
Alternative Form
a∈(−1.172988,0.857114)
Evaluate
6a2−210−6a<0
Find the domain
More Steps
Evaluate
10−6a≥0
Move the constant to the right side
−6a≥0−10
Removing 0 doesn't change the value,so remove it from the expression
−6a≥−10
Change the signs on both sides of the inequality and flip the inequality sign
6a≤10
Divide both sides
66a≤610
Divide the numbers
a≤610
Cancel out the common factor 2
a≤35
6a2−210−6a<0,a≤35
Move the expression to the right side
−210−6a<−6a2
Divide both sides
10−6a>3a2
Raise both sides of the inequality to the power of 2
10−6a>(3a2)2
Evaluate the power
More Steps
Evaluate
(3a2)2
To raise a product to a power,raise each factor to that power
32(a2)2
Evaluate the power
9(a2)2
Evaluate the power
More Steps
Evaluate
(a2)2
Multiply the exponents
a2×2
Multiply the terms
a4
9a4
10−6a>9a4
Move the expression to the left side
10−6a−9a4>0
Rewrite the expression
10−6a−9a4=0
Find the critical values by solving the corresponding equation
a≈−1.172988a≈0.857114
Determine the test intervals using the critical values
a<−1.172988−1.172988<a<0.857114a>0.857114
Choose a value form each interval
a1=−2a2=0a3=2
To determine if a<−1.172988 is the solution to the inequality,test if the chosen value a=−2 satisfies the initial inequality
More Steps
Evaluate
10−6(−2)−9(−2)4>0
Simplify
More Steps
Evaluate
10−6(−2)−9(−2)4
Multiply the numbers
10+12−9(−2)4
Multiply the terms
10+12−144
Calculate the sum or difference
−122
−122>0
Check the inequality
false
a<−1.172988 is not a solutiona2=0a3=2
To determine if −1.172988<a<0.857114 is the solution to the inequality,test if the chosen value a=0 satisfies the initial inequality
More Steps
Evaluate
10−6×0−9×04>0
Any expression multiplied by 0 equals 0
10−0−9×04>0
Simplify
More Steps
Evaluate
10−0−9×04
Calculate
10−0−9×0
Any expression multiplied by 0 equals 0
10−0−0
Removing 0 doesn't change the value,so remove it from the expression
10
10>0
Check the inequality
true
a<−1.172988 is not a solution−1.172988<a<0.857114 is the solutiona3=2
To determine if a>0.857114 is the solution to the inequality,test if the chosen value a=2 satisfies the initial inequality
More Steps
Evaluate
10−6×2−9×24>0
Simplify
More Steps
Evaluate
10−6×2−9×24
Multiply the numbers
10−12−9×24
Multiply the terms
10−12−144
Subtract the numbers
−146
−146>0
Check the inequality
false
a<−1.172988 is not a solution−1.172988<a<0.857114 is the solutiona>0.857114 is not a solution
The original inequality is a strict inequality,so does not include the critical value ,the final solution is −1.172988<a<0.857114
−1.172988<a<0.857114
Check if the solution is in the defined range
−1.172988<a<0.857114,a≤35
Solution
−1.172988<a<0.857114
Alternative Form
a∈(−1.172988,0.857114)
Show Solution
