Question
Solve the inequality
Solve the inequality by testing the values in the interval
Solve for v
−43≤v≤43
Alternative Form
v∈[−43,43]
Evaluate
v×v3−2≤1
Multiply the terms
More Steps

Evaluate
v×v3
Use the product rule an×am=an+m to simplify the expression
v1+3
Add the numbers
v4
v4−2≤1
Move the expression to the left side
v4−2−1≤0
Subtract the numbers
v4−3≤0
Rewrite the expression
v4−3=0
Move the constant to the right-hand side and change its sign
v4=0+3
Removing 0 doesn't change the value,so remove it from the expression
v4=3
Take the root of both sides of the equation and remember to use both positive and negative roots
v=±43
Separate the equation into 2 possible cases
v=43v=−43
Determine the test intervals using the critical values
v<−43−43<v<43v>43
Choose a value form each interval
v1=−2v2=0v3=2
To determine if v<−43 is the solution to the inequality,test if the chosen value v=−2 satisfies the initial inequality
More Steps

Evaluate
(−2)4−2≤1
Subtract the numbers
More Steps

Evaluate
(−2)4−2
Simplify
24−2
Evaluate the power
16−2
Subtract the numbers
14
14≤1
Check the inequality
false
v<−43 is not a solutionv2=0v3=2
To determine if −43<v<43 is the solution to the inequality,test if the chosen value v=0 satisfies the initial inequality
More Steps

Evaluate
04−2≤1
Simplify
More Steps

Evaluate
04−2
Calculate
0−2
Removing 0 doesn't change the value,so remove it from the expression
−2
−2≤1
Check the inequality
true
v<−43 is not a solution−43<v<43 is the solutionv3=2
To determine if v>43 is the solution to the inequality,test if the chosen value v=2 satisfies the initial inequality
More Steps

Evaluate
24−2≤1
Subtract the numbers
More Steps

Evaluate
24−2
Evaluate the power
16−2
Subtract the numbers
14
14≤1
Check the inequality
false
v<−43 is not a solution−43<v<43 is the solutionv>43 is not a solution
The original inequality is a nonstrict inequality,so include the critical value in the solution
−43≤v≤43 is the solution
Solution
−43≤v≤43
Alternative Form
v∈[−43,43]
Show Solution
