Question

How do you solve `-1 <= x-3 <= 5`?

Answer 1

Solve for `x` by adding `+3` to all three parts of the compound the inequality.

`2 <= x <=8`

Explanation:

`-1 <= x-3 <-5" "`add 3 to each part

`-1 color(red)(+ 3) <= x -3 color(red)(+ 3) <= 5 color(red)(+3)" "` Doing all of the addition results in

`+2 <= x <= 8" "x` is now isolated in the middle

`2 <= x <=8" "` this is the final answer

Answer 2

`2 <=x<=8`

Explanation:

`-1 <= x-3 <=5`

You can break the inequality up into two parts, work with them separately, and combine them at the end.

`color(red)(-1 <= x-3 )<=5" "and" " -1 <= color(blue)(x-3 <=5)`

`color(red)(-1 <= x-3 )color(white)(........................................)color(blue)(x-3 <=5)`

Isolate x on the right side `color(white)(................)` isolate x on the left side
`color(red)(-1 +3 <= x )color(white)(........................................)color(blue)(x <=5+3)`

`color(white)(.........)color(red)(2<= x )color(white)(.........................................)color(blue)(x <=8)`

Now combine the two parts with one `x`

`color(white)(...............................)color(red)(2<= )x color(blue)(<=8)`