Question

How do you solve `0.4( y + 9) < - 1.2( 8- y )`?

Answer 1

See the entire solution process below:

Explanation:

First, expand the terms within parenthesis on each side of the inequality:

`(0.4 xx y) + (0.4 xx 9) < (-1.2 xx 8) + (-1.2 xx -y)`

`0.4y + 3.6 < -9.6 + 1.2y`

Next, subtract `color(red)(0.4y)` and add `color(blue)(9.6)` to each side of the inequality to isolate the `y` term while keeping the inequality balanced:

`0.4y + 3.6 - color(red)(0.4y) + color(blue)(9.6) < -9.6 + 1.2y - color(red)(0.4y) + color(blue)(9.6)`

`0.4y - color(red)(0.4y) + 3.6 + color(blue)(9.6) < -9.6 + color(blue)(9.6) + 1.2y - color(red)(0.4y)`

`0 + 13.2 < 0 + 0.8y`

`13.2 < 0.8y`

Now, divide each side of the inequality by `color(red)(0.8)` to solve for `y` while keeping the inequality balanced:

`13.2/color(red)(0.8) < (0.8y)/color(red)(0.8)`

`16.5 < (color(red)(cancel(color(black)(0.8)))y)/cancel(color(red)(0.8))`

`16.5 < y`

Last, to solve in terms of `y` we need to reverse or "flip" the inequality:

`y > 16.5`