Question

How do you solve `0\leq \frac { x + 3} { 2} < 6`?

Answer 1

See the entire solution process below:

Explanation:

First, multiply each segment of the system if inequalities by `color(red)(2)` in order to eliminate the fraction while keeping the system balanced:

`color(red)(2) xx 0 <= color(red)(2) xx (x + 3)/2 < color(red)(2) xx 6`

`0 <= cancel(color(red)(2)) xx (x + 3)/color(red)(cancel(color(black)(2))) < 12`

`0 <= x + 3 < 12`

Now, subtract `color(red)(3)` from each segment of the system of inequalities to solve for `x` while keeping the system balanced:

`0 - color(red)(3) <= x + 3 - color(red)(3) < 12 - color(red)(3)`

`-3 <= x + 0 < 9`

`-3 <= x < 9`