Question

I have two different questions.

what is the set built notation of -11x-24<27-10x

and

write the slope intercept equation for the line with slope -5/6 and y intercept (0,4)

Answer 1

-11x-24<27-10x
-11x + 10x < 27 + 24
-x < 51
x > -51

I will let you put into the notation you are familiar with

second one:
since you are given the slope and the y-intercept, the equation can be simply stated as

y = (-5/6)x + 4

Answer 2

-11x-24 < 27-10x
combine similar terms:
-11x + 10x < 27 + 24
*when transposing terms to other side of equation, the sign must become the opposite*
then,
-x < 51
multiply by -1 to get positive x:
x > -51
*note that when all terms are multiplied or divided by a NEGATIVE number, the inequality sign becomes the opposite*
thus x is all real number greater than -51 or (-51, +infinity)

for the second question,
slope-intercept form is:
y = mx + b
where b is the y-intercept (y-coordinate of the y-intercept) and m is the slope,, thus:
y = (-5/6)x + 4

hope this helps. :)