# Math Help - Set of values of X

1. ## Set of values of X

Sketch the graph of $y=\frac{(2(x+a))}{(x-1)}$, where $a>2$. Hence find the set of values of x such that $\frac{2(x+a)}{x-1}\leqslant |x+a|$

2. Originally Posted by Punch
Sketch the graph of y=\frac{(2(x+a))}{(x-1)}, where $a>2$. Hence find the set of values of x such that \frac{2(x+a)}{x-1}≤|x+a|
And what did your graph tell you?

-Dan

3. Originally Posted by topsquark
And what did your graph tell you?

-Dan
From my understanding, the 2 graphs would intersect at 2 points, but i doubt this could help in anyway. Is there something I overlooked?

4. Originally Posted by Punch
From my understanding, the 2 graphs would intersect at 2 points, but i doubt this could help in anyway. Is there something I overlooked?
Originally Posted by Punch
Sketch the graph of $y=\frac{(2(x+a))}{(x-1)}$, where $a>2$. Hence find the set of values of x such that $\frac{2(x+a)}{x-1}\leqslant |x+a|$
They intersect twice. Good. Now look at the inequality again. You are looking for all points on the 2(x + a)/(x - 1) curve that are lower on the graph (or equal to) the graph of |x + a|. So what parts of the function 2(x + a)/(x - 1) are below the lines?

-Dan

5. Originally Posted by topsquark
They intersect twice. Good. Now look at the inequality again. You are looking for all points on the 2(x + a)/(x - 1) curve that are lower on the graph (or equal to) the graph of |x + a|. So what parts of the function 2(x + a)/(x - 1) are below the lines?

-Dan
but i cant find out since i cant draw the graph of |x+a| without knowing the value of a