college algebra question

[camilus]

Solve the following inequality and express the solution set in interval notation.

http://www.webassign.net/www24/symImages/4/6/aaf987edafbf00c172f8cfaf01966c.gif

[camilus]

I got most of the answer right, except the lower interval.

the answer is:

( ??? , 4 )

the question is find the ???

it is a negative number is like -4x10^8, and I have narrowed it down to somewhere around -3.98558x10^8, but whata fuck, how the hell m I supposed to get EXACT number???

[Pete]

Personally, I'd begin by graphing both sides, finding the intersections, and looking at the domain for which the inequality is true.

Actually, that's as hard as it gets, I think.

[Pete]

Get the exact intersection by solving for 1/(x-4) = 1/(x+7).

[Pete]

Wait... there are no intersections. Inspecting the graphs indicates that the inequality is true for -7 <= x <= 4

[camilus]

Personally, I'd begin by graphing both sides, finding the intersections, and looking at the domain for which the inequality is true.

Actually, that's as hard as it gets, I think.

I have a pretty good graphing calculator, and I graphed them and it could not find an intersection.

Get the exact intersection by solving for 1/(x-4) = 1/(x+7).

cmon Pete, I know you're one of that math gurus here but that was retarded..

try it

1/(x-4)=1/(x+7) can be rewritten as x+7=x+4 (cross multiply)

Im assuming you can see the contradiction screaming at you...

[camilus]

yeah, it was -7

thanks for the quick help man.

[camilus]

ANOTHER ONE!!

Solve the following inequality and express the solution set in interval notation.

http://www.webassign.net/www28/symImages/e/2/572f4d8ce2cc5d1b729a33406a243e.gif

[camilus]

PLEASE SOMEONE HELP WITH THIS ONE!!!! its due in like 20 minutes!!!!!

[Kadark]

I just worked it out:

x < -13

Do you want me to explain?


Kadark

[Kadark]

|(x - 1)/(x + 27)| > 1

Remove the absolute value sign by switching the "greater than" value, and making the positive one into a negative one.

(x - 1)/(x + 27) < -1

Multiply (-1) by (x + 27).

(x - 1) < -x - 27

Carry the (-1) over.

x < -x - 26

Bring the (-x) over.

2x < -26

Divide by two.

x < -13

For these types of questions, you're supposed to solve it the way I just showed, in addition to this way:

(x - 1)/(x + 27) > 1

You're supposed to multiply 1 by the left-hand side's denominator, but that inevitably leads to the x-terms canceling out. Therefore, you omit them from your final answer.

Note: when you reinsert the -13 into your original inequality, the answer will come out as a negative value. However, that problem will be solved by the absolute value signs, making your answer greater than positive one (for all values of x that are less than -13).

I haven't done these in a while, so I hope I did this right.


Kadark

[Pete]

Hi Kadark,
|(x - 1)/(x + 27)| > 1

Remove the absolute value sign by switching the "greater than" value, and making the positive one into a negative one.

(x - 1)/(x + 27) < -1

Multiply (-1) by (x + 27).

(x - 1) < -x - 27
I was doing this the same way, but realised that you have to consider the sign of the multiplier when you multiply or divide both sides of an inequality. i.e. if (x+27) is negative, the direction of the inequality will reverse.
So, at this step, you get two sets of inequalities (I hope this notation makes sense?):
\left[x\ >\ -27 \\ x-1\ <\ -x-27 \right.

\left[x\ <\ -27 \\ x-1\ >\ -x-27 \right.

Carrying on, you end up with:
\left[x\ >\ -27 \\ x\ <\ -13 \right.

\left[x\ <\ -27 \\ x\ >\ -13 \right.

The second pair has no solution, leaving us with only the first:

-27 < x < -13

For these types of questions, you're supposed to solve it the way I just showed, in addition to this way:

(x - 1)/(x + 27) > 1

You're supposed to multiply 1 by the left-hand side's denominator, but that inevitably leads to the x-terms canceling out. Therefore, you omit them from your final answer.
The same applies to this case, resulting in the equality being true for all x < -27.
... which exactly negates the range eliminated in the previous step, except for x=27 (which makes sense, because there is a singularity there).

So the final answer will be:
x < -27
-27 < x < -13


...I hope that makes sense!