What is the inequality of x(x-8)/x^2-7x-98 is all less than or equal to 0?

Question

THE ANSWER MUST BE IN INTERVAL NOTATION....

Answer 1

x(x-8) / (x^2-7x-98) ≤ 0

[x(x-8)] / [(x-14)(x+7)] ≤ 0

the critical numbers are: -7,0,8,14

the signs of the intervals are:

..... -7 ........ 0 ...... 8 ...... 14 ........
(+) ...... (-) ..... (+) .... (-) ...... (+)

choose the negative...
thus
(-7, 0] U [8 , 14)


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Answer 2

(-7,0] U [8,14)

I looked at the factored form of the expression:

[x(x-8)] / [(x-14)(x+7)]

and placed the critical values (where a factor =0) on a number line: -7, 0, 8, 14.

Then I tested each interval to see if it were positive or negative. the 0 and 8 endpoints are closed, but the -7 and 14 endpoints are open because we don't want 0 in the denominator.

that's it! hope it helps.

Answer 3

It is unclear whether the expression x^2-7x-98 should be (x^2-7x-98)
x(x-8)/(x-14)(x+7) <0
x(x-8) < x^2-7x-98
x^2-8x < x^2-7x-98
x^2 cancels out
-8x+7x < -98
-x < -98
x > 98 ( reversing the sign on both sides will change > to < and < to >.

Answer 4

x(x-8)/(x^2-7x-98) <= 0
x(x-8)/[(x-14)(x+7)] <= 0
(-7, 0] U [8, infinity)