How do you solve #(16.5+3t)/3=(0.9-t)/-5#?

2 Answers
Feb 20, 2017

Answer:

See the entire solution process below:

Explanation:

First, multiply each side of the equation by #color(red)(15)# to eliminate the fractions while keeping the equation balanced:

#color(red)(15) xx (16.5 + 3t)/3 = color(red)(15) xx (0.9 - t)/(-5)#

#cancel(color(red)(15)) 5 xx (16.5 + 3t)/color(red)(cancel(color(black)(3))) = cancel(color(red)(15)) (-3) xx (0.9 - t)/color(red)(cancel(color(black)(-5)))#

#5(16.5 + 3t) = -3(0.9 - t)#

Next, expand the terms within parenthesis:

#(5 xx 16.5) + (5 xx 3t) = (-3 xx 0.9) - (-3 xx t)#

#82.5 + 15t = -2.7 + 3t#

Then, subtract #color(blue)(82.5)# and #color(red)(3t)# from each side of the equation to isolate the #t# term while keeping the equation balanced:

#82.5 + 15t - color(blue)(82.5) - color(red)(3t) = -2.7 + 3t - color(blue)(82.5) - color(red)(3t)#

#82.5 - color(blue)(82.5) + 15t - color(red)(3t) = -2.7 - color(blue)(82.5) + 3t - color(red)(3t)#

#0 + 12t = -85.2 + 0#

#12t = -85.2#

Now, divide each side of the equation by #color(red)(12)# to solve for #t# while keeping the equation balanced:

#(12t)/color(red)(12) = -85.2/color(red)(12)#

#(color(red)(cancel(color(black)(12)))t)/cancel(color(red)(12)) = -7.1#

#t = -7.1#

Feb 20, 2017

Answer:

#t=-7.1#

Explanation:

#(16.5+3t)/3=(0.9-t)/-5#

multiply both sides by-15

#:.-15((16.5+3t))/3=-15((0.9-t))/-5#

#:.-5(16.5+3t)=3(0.9-t)#

#:.-82.5-15t=2.7-3t#

#:.-15t+3t=2.7+82.5#

#:.-12t=85.2#

#:.-t=85.2/12#

#:.t=-85.2/12#

#:.t=-7.1#

check:

substitute# t=-7.1#

#((16.5+3(-7.1)))/3=((0.9-(-7.1)))/-5#

#:.(16.5-21.3)/3=(0.9+7.1)/(-5)#

#:.-4.8/3=8/-5#

#:.-1.6=-1.6#