How do you solve 2/(x+1)>&= 5?

Question

i did the work and graphed it on a calculator, and i think i have the right answer... (-(3/5), infinity)

Answer 1

The easiest way to do this sort of problem by hand is to write it as an inequality involving zero. In this case you have,

2/(x+1)-5>=0

2/(x-1)-5(x-1)/(x-1)>=0
[2-5(x-1)]/(x-1)>=0
(7-5x)/(x-1)>=0

Now remember: you must _never_ multiply an inequality by an unknown because you don't know if an unknown is positive or negative so you don't know if you are supposed to flip the inequality or not. Instead, make a sign chart.

To do so, draw a real number line.

Label the zeros of the terms in the expression: In this case, 7/5 and 1.

Notice that the quotient is negative when the numerator is positive and the denominator is negative or when the numerator is negative and the denominator is positive. Similarly, the quotient is positive when both the numerator and denominator are negative or positive. In this case,

(7-5x)/(x-1) is negative if x >7/5

(7-5x)/(x-1) is positive if 1
(7-5x)/(x-1) is negative if x<1

Thus, (7-5x)/(x-1) is greater than or equal to zero when 1
It is 0 at 7/5 so you include 7/5; you discard the 1 because division by 0 is always undefined.

In interval notation, your answer would be (1,7/5].

Note: Brackets mean to include the numbers; parents mean to not include the number.

Good luck! :)

Answer 2

2/(x+ 1) >= 5

Assuming that x cannot be -1 or less than -1, since those values lead (x+1) to zero or switch the sign,

2 >= 5(x+ 1)
2 >= 5x+ 5
2- 5 >= 5x
-3 >= 5x
-3/5 >= x--- --- ---> x <= -3/5

However x less than or equal -3/5 implies that x could be -1 or less. But remember that we assumed x couldn't be -1 or below. So the answer to this problem is -1 < x <= -3/5.

Answer 3

try any big #: it won't work! The problem is, we don't know if x+1 is positive or negative. But then, if it's negative, the fraction can't be more than 5 (if we didn't know this, we'd have to coinsider both cases.) So it must be positive. Since x > -1, then we DON"T change sign when multiplying by x + 1. So the solution will be from -1 (excluding) to -3/5 (including).

Answer 4

it's (-3(3/5))