Question

How do you solve `-3( y + 2.5) = 6.9- 4.2y`?

Answer 1

See a solution process below:

Explanation:

First, expand the terms on the left side of the equation by multiplying each term within the parenthesis by the term outside the parenthesis:

`color(red)(-3)(y + 2.5) = 6.9 - 4.2y`

`(color(red)(-3) xx y) + (color(red)(-3) xx 2.5) = 6.9 - 4.2y`

`-3y - 7.5 = 6.9 - 4.2y`

Next, add `color(red)(7.5)` and `color(blue)(4.2y)` to each side of the equation to isolate the `y` term while keeping the equation balanced:

`-3y - 7.5 + color(red)(7.5) + color(blue)(4.2y) = 6.9 - 4.2y + color(red)(7.5) + color(blue)(4.2y)`

`-3y + color(blue)(4.2y) - 7.5 + color(red)(7.5) = 6.9 + color(red)(7.5) - 4.2y + color(blue)(4.2y)`

`(-3 + color(blue)(4.2))y - 0 = 14.4 - 0`

`1.2y = 14.4`

Now, divide each side of the equation by `color(red)(1.2)` to solve for `y` while keeping the equation balanced:

`(1.2y)/color(red)(1.2) = 14.4/color(red)(1.2)`

`(color(red)(cancel(color(black)(1.2)))y)/cancel(color(red)(1.2)) = 12`

`y = 12`