The inequality is

write 7 as 7b/b to have all the expressions in common denominator:






here b=1 is a root and b=0 is not in the domain of the expression, but it still has an effect in the sign of the expression.
the sign table of

is :
+++++++[0] --------[1] +++++
this means that for values of b to the left of 0 and to the right of 1, the expression is positive, and for values of b in (0, 1), the expression is negative.
that is

for b∈(0, 1)
Answer: (0, 1)
The answer for this question is 3(x+4)=1/2x-8
As shown in the figure below the answer is the last option:

The roots of the polynomial in the denominator are:


So, the inequality can be written as follows:

From this inequality we can study the signs and get the same conclusion just as shows the graph.
Smaller leg = x
longer leg = y
hypotenuse = z
y=x+7
z=x+8
due to

but x cannot be -3
so smaller leg is 5 inches
then longer leg = 5+7 = 12 inches
and hypotenuse = 5+8 = 13 inches