How do you solve #\frac { 3} { 5} z + 1= - 14#?

↳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
ceenik
Apr 24, 2017

#z =-25#

Explanation:

#\frac { 3} { 5} z + 1= - 14#

First move the #1# to the other side so we can begin to isolate z

#\frac { 3} { 5} z = - 14 -1#

#\frac { 3} { 5} z = -15#

Now divide both sides by #3/5# so we can get the value of #z#

#z =-15 -: 3/5#
[Remember there is a #1# under every number, we just don't write it because we know it is there.]

#z =-15/1 -: 3/5#

Flip #3/5# so we can multiply

#z =-15/1 * 5/3#

Now just multiply across

#z =-(15*5)/(1*3)#

#z =-75/3#

and divide...

#z =-25#

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