Question

How do you solve `11\leq 3x - 1< 19`?

Answer 1

See the entire solution process below:

Explanation:

First, add `color(red)(1)` to each segment of the system of inequalities to isolate the `x` term while keeping the system balanced:

`11 + color(red)(1) <= 3x - 1 + color(red)(1) < 19 + color(red)(1)`

`12 <= 3x - 0 < 20`

`12 <= 3x < 20`

Now, divide each segment by `color(red)(3)` to solve for `x` while keeping the system balanced:

`12/color(red)(3) <= (3x)/color(red)(3) < 20/color(red)(3)`

`4 <= (color(red)(cancel(color(black)(3)))x)/cancel(color(red)(3)) < 20/3`

`4 <= x < 20/3`