Question

How do you solve `12\geq 4+ \frac { 5x } { 8}`?

Answer 1

See a solution process below:

Explanation:

First, subtract `color(red)(4)` from each side of the inequality to isolate the `x` term while keeping the inequality balanced:

`-color(red)(4) + 12 >= -color(red)(4) + 4 + (5x)/8`

`8 >= 0 + (5x)/8`

`8 >= (5x)/8`

Now, multiply each side of the inequality by `color(red)(8)/color(blue)(5)` to solve for `x` while keeping the inequality balanced:

`color(red)(8)/color(blue)(5) xx 8 >= color(red)(8)/color(blue)(5) xx (5x)/8`

`64/5 >= cancel(color(red)(8))/cancel(color(blue)(5)) xx (color(blue)(cancel(color(black)(5)))x)/color(red)(cancel(color(black)(8)))`

`64/5 >= x`

To write the solution in terms of `x` we can reverse or "flip" the entire inequality:

`x <= 64/5`