find the x intercept and solve the equation?

Question

a)graph the following and find the x- intercept.

b)set y=0 and solve for the resulting equation.

     y=10(3/(x+4)-6/x

 

I really dont understand this question.I think that the xintercept is -8.And that for part be i have to wrotte this y=0(x/(x+4)-x/6 or maybe like this 0=10(3/(x+4)-6/x.But i am not sure.Can someone please explain to me this question?

 

Thank you.

Answer 1

To find the X-intercept, one would wish to find where the line intersects the X-axis.  For any equation referring to X and another variable, say Y, one is looking for the solution to the equation where Y=0.  Since when we are looking at a line plotted on a graph, one can imagine an example such as:

 

There are 2 values measured: one vertical height which is referred to as Y, and the other horizontal distance which is referred to as X.  When the Height, or the Y value is 0, the line has crashed into land and its position is measured by a 0 height and some distance, or X value, from the reference point.

 

If there is a solution to Y=0, the intercept will be of the form (X,Y) and look like (X,0) for some value X.

Likewise, one will do the opposite for the Y-intercept.  One will solve for X=0 and the solution will be of the form (X,Y) and look like (0,Y) for some value Y.

 

So of the two equations you derived, the second one was the one you wanted.  

 

So when solving for Y=0, we arrive at:

 

0=10(3/(X+4)-6/X)

(1/10)*(0=10(3/(X+4)-6/X))

0=3/(X+4)-6/X)

6/X=3/(X+4)

6(X+4)=3X

6X+24=3X

3X=-24

X=-8

 

Therefore the X-intercept is at (-8,0).

This is the point at which the line crosses the X-axis.  You were correct.

I hope this explanation has been helpful.

Answer 2

a)graph y=10(3/(x+4)-6/x and find the x- intercept.

 

I'll assume a parenthesis at the end:

 

y=10(3/(x+4)-6/x) = 30/(x+4) - 60/x

 

Notice that because you can't divide by zero: x ≠ -4 or 0

Indeed, the graph will have vertical asymptotes at x = -4 and x = 0

 

As x → -4^-, y → -∞.  (Substitute x=-4-10^(-100) and solve for y.) 

As x → -4⁺, y → +∞. (Substitute x=-4+10^(-100) and solve for y.)

As x → 0^-, y → +∞. (Substitute x=0-10^(-100) and solve for y.)
As x → 0⁺, y → -∞. (Substitute x=0+10^(-100) and solve for y.)

 

Let's combine the fractions:

 

y = 30x/(x(x+4)) - 60(x+4)/(x(x+4))

 

y = -(30x + 240)/(x(x+4))

 

y = - 30(x + 8)/(x(x+4))

 

As x → +∞, y → -30/(+∞) → 0^-; i.e., y approaches the x-axis from below.

As x → -∞, y → -30/(-∞) → 0⁺; i.e., y approaches the x-axis from above.

The x intercept occurs when y = 0 = - 30(x + 8)/(x(x+4)): i.e., x = -8

 

b)set y=0 and solve for the resulting equation.

 

Did it to find x intercept.

 

http://www.dropbox.com/s/qpl3iz1k22s8q44/sks23cu14012701.png

is a GeoGebra graph.