How do you solve #T = (3/10)(Z - 12,000)# for Z?

1 Answer
Jun 4, 2016

Answer:

#Z=10/3(T+3600)#

Explanation:

Given,

#T=3/10(Z-12000)#

Use the distributive property, #color(red)a(color(blue)b+color(purple)c)=color(red)acolor(blue)b+color(red)acolor(purple)c#, to expand the right side.

#T=3/10(Z)+3/10(-12000)#

#T=3/10Z+(3xx-12000)/10#

#T=3/10Z-36000/10#

#T=3/10Z-3600#

Isolate for #Z#. Start by adding #3600# to both sides.

#Tcolor(white)(i)color(red)(+3600)=3/10Z-3600color(white)(i)color(red)(+3600)#

#T+3600=3/10Z#

Divide both sides by #3/10#.

#color(red)((color(black)(T+3600))/(3/10))=color(red)((color(black)(3/10Z))/(3/10))#

#color(red)((color(black)(T+3600))/(3/10))=color(red)((color(black)(color(blue)cancelcolor(black)(3/10)Z))/(color(blue)cancelcolor(red)(3/10)))#

Note: Recall that dividing by a fraction is the same as multiplying by its reciprocal!

#Z=color(green)(|bar(ul(color(white)(a/a)color(black)(10/3(T+3600))color(white)(a/a)|)))#