Question

How do you solve `0. 5 t + 0 . 2 5 ( t + 1 6 ) = 4 + . 1 5 t`?

Answer 1

See a solution process below:

Explanation:

First, expand the term in parenthesis by multiplying each term within the parenthesis by the term outside the parenthesis:

`0.5t + color(red)(0.25)(t + 16) = 4 + 0.15t`

`0.5t + (color(red)(0.25) * t) + (color(red)(0.25) * 16) = 4 + 0.15t`

`0.5t + 0.25t + 4 = 4 + 0.15t`

`(0.5 + 0.25)t + 4 = 4 + 0.15t`

`0.75t + 4 = 4 + 0.15t`

Next, subtract `color(red)(4)` and `color(blue)(0.15t)` from each side of the equation to isolate the `t` term while keeping the equation balanced:

`0.75t + 4 - color(red)(4) - color(blue)(0.15t) = 4 + 0.15t - color(red)(4) - color(blue)(0.15t)`

`0.75t - color(blue)(0.15t) + 4 - color(red)(4) = 4 - color(red)(4) + 0.15t - color(blue)(0.15t)`

`(0.75 - color(blue)(0.15))t + 0 = 0 + 0`

`0.6t = 0`

Now, divide each side of the equation by `color(red)(0.6)` to solve for `t` while keeping the equation balanced:

`(0.6t)/color(red)(0.6) = 0/color(red)(0.6)`

`(color(red)(cancel(color(black)(0.6)))t)/cancel(color(red)(0.6)) = 0`

`t = 0`