Question

How do you solve `30< 5( x + 6) < 85`?

Answer 1

See the entire solution process below:

Explanation:

First, divide each segment of the system of equation by `color(red)(5)` to eliminate the term outside the parenthesis while keeping the system balanced:

`30/color(red)(5) < (5(x + 6))/color(red)(5) < 85/color(red)(5)`

`6 < (color(red)(cancel(color(black)(5)))(x + 6))/cancel(color(red)(5)) < 17`

`6 < x + 6 < 17`

Now, subtract `color(red)(6)` from each segment to solve for `x` while keeping the system balanced:

`6 - color(red)(6) < x + 6 - color(red)(6) < 17 - color(red)(6)`

`0 < x + 0 < 11`

`0 < x < 11`

Or

`x > 0` and `x < 11`

Or, in interval notation:

`(0, 11)`