Question

Solve the inequality
x 15
--- + ---- <= 4
4 x+7
for domain

Answer 1

Multiply both sides by 4(x+7)

Answer 2

I did but that led me to x^2-9x+172 and that doesnt seem right

Answer 3

\[x(x+7) + 4(15) \le 4*4(x+7)\]
\[\implies x^2 + 7x + 60 \le 16x + 112\]
\[\implies x^2 -9x - 52 \le 0\]

Answer 4

So solve the quadratic for 0 and you have your solutions.

Answer 5

I got -9 and 13......how do I use those to find the domain?

Answer 6

that is the domain

Answer 7

its an inequality theres a different way to solve for the domain

Answer 8

No, factor it.

Answer 9

\[(x -13)(x+4) \le 0\]

Answer 10

That means that one of those two factors must be negative (but not both) for the relation to hold.

Answer 11

So what values of x will yield a negative in one of either (x-13) or (x+4) but not both.

Answer 12

between -4 and 13?

my options for an answer are

A. (-7,-4] U [13, inf)
B. (-inf,-7)U(-4,13)
C. (-inf,-7]U[-4,13)
D. (-inf,-7)U[-4,13]
E. (-7,-4)U(13,inf)

Answer 13

If x is between -4 and 13 (say maybe x=0) we have one positive and one negative, so that seems reasonable.

Answer 14

We did get rid of a factor of x+7 though when we solved it, so I think your answer is probably D.