2x+1/x+1 (is less than or equal to) 2
what is the solution of the inequality?
If (2x+1)/(x+1) = 2, then
2x +1 = 2x +2
which can never happen.
If x>-1, 2x +1 <= 2x + 2
which is always true
If x<-1 2x +1 >= 2x =2
which is never true.
Therefore x > -1 is the answer.
x = -1 is not allowed
To find the solution of the inequality 2x + 1/x + 1 <= 2, we need to rearrange it and solve for x.
First, let's get rid of the fraction by multiplying both sides of the inequality by x + 1:
(x + 1)(2x + 1)/(x + 1) <= 2(x + 1)
This simplifies to:
2x + 1 <= 2(x + 1)
Expanding the right side:
2x + 1 <= 2x + 2
Next, let's isolate the variable x on one side of the inequality. Subtracting 2x from both sides:
1 <= 2
Since 1 is always less than or equal to 2, this inequality is true for all values of x.
Therefore, the solution to the inequality 2x + 1/x + 1 <= 2 is all real numbers.