Question
Solve the inequality
Solve the inequality by testing the values in the interval
Solve for r
r∈R
Alternative Form
All real solution
Evaluate
r×r3−16≥−17
Multiply the terms
More Steps

Evaluate
r×r3
Use the product rule an×am=an+m to simplify the expression
r1+3
Add the numbers
r4
r4−16≥−17
Move the expression to the left side
r4−16−(−17)≥0
Subtract the numbers
More Steps

Evaluate
−16−(−17)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
−16+17
Add the numbers
1
r4+1≥0
Rewrite the expression
r4+1=0
Move the constant to the right-hand side and change its sign
r4=0−1
Removing 0 doesn't change the value,so remove it from the expression
r4=−1
Since the left-hand side is always positive or 0,and the right-hand side is always negative,the statement is false for any value of r
r∈/R
There are no key numbers,so choose any value to test,for example r=0
r=0
Solution
More Steps

Evaluate
04−16≥−17
Simplify
More Steps

Evaluate
04−16
Calculate
0−16
Removing 0 doesn't change the value,so remove it from the expression
−16
−16≥−17
Check the inequality
true
r∈R
Alternative Form
All real solution
Show Solution
