Question

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

Answer 1

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`

Answer 2

`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`