Question
Solve the inequality
0.244162<z<2.303301
Alternative Form
z∈(0.244162,2.303301)
Evaluate
6z4−82z<−20
Move the expression to the left side
6z4−82z−(−20)<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
6z4−82z+20<0
Rewrite the expression
6z4−82z+20=0
Factor the expression
2(3z4−41z+10)=0
Divide both sides
3z4−41z+10=0
Calculate
z≈2.303301z≈0.244162
Determine the test intervals using the critical values
z<0.2441620.244162<z<2.303301z>2.303301
Choose a value form each interval
z1=−1z2=1z3=3
To determine if z<0.244162 is the solution to the inequality,test if the chosen value z=−1 satisfies the initial inequality
More Steps
Evaluate
6(−1)4−82(−1)<−20
Simplify
More Steps
Evaluate
6(−1)4−82(−1)
Evaluate the power
6×1−82(−1)
Any expression multiplied by 1 remains the same
6−82(−1)
Simplify
6−(−82)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
6+82
Add the numbers
88
88<−20
Check the inequality
false
z<0.244162 is not a solutionz2=1z3=3
To determine if 0.244162<z<2.303301 is the solution to the inequality,test if the chosen value z=1 satisfies the initial inequality
More Steps
Evaluate
6×14−82×1<−20
Simplify
More Steps
Evaluate
6×14−82×1
1 raised to any power equals to 1
6×1−82×1
Any expression multiplied by 1 remains the same
6−82×1
Any expression multiplied by 1 remains the same
6−82
Subtract the numbers
−76
−76<−20
Check the inequality
true
z<0.244162 is not a solution0.244162<z<2.303301 is the solutionz3=3
To determine if z>2.303301 is the solution to the inequality,test if the chosen value z=3 satisfies the initial inequality
More Steps
Evaluate
6×34−82×3<−20
Simplify
More Steps
Evaluate
6×34−82×3
Multiply the terms
486−82×3
Multiply the numbers
486−246
Subtract the numbers
240
240<−20
Check the inequality
false
z<0.244162 is not a solution0.244162<z<2.303301 is the solutionz>2.303301 is not a solution
Solution
0.244162<z<2.303301
Alternative Form
z∈(0.244162,2.303301)
Show Solution