How do you solve and write the following in interval notation: #6-8(y+3) + 5y > 5y-(2y-5)+13#?

↳Redirected from "Suppose that I don't have a formula for #g(x)# but I know that #g(1) = 3# and #g'(x) = sqrt(x^2+15)# for all x. How do I use a linear approximation to estimate #g(0.9)# and #g(1.1)#?"
1 Answer
Shantelle
Jul 24, 2018

#y < -93#
Interval notation: #(-oo, -93)#

Explanation:

#6 - 8(y+3) + 5y > 57 - (2y - 5) + 13#

Distribute/expand:
#6 - 8y - 24 + 5y > 57 - 2y + 5 + 13#

Simplify each side:
#-18 - 3y > 75 - 2y#

Add #color(blue)(3y)# to both sides and subtract #color(blue)(75)# from both sides:
#-93 > y#

Therefore,
#y < -93#

Interval notation: #(-oo, -93)#

The parenthesis means that the numbers are between negative infinity and #-93#, but not including #-93#. It's anything less than #-93#.

Hope this helps!

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