Question

How do you solve `-2\leq \frac { 2x - 1} { 4} < 2`?

Answer 1

See a solution process below:

Explanation:

First, multiply each segment of the system of inequalities by `color(red)(4)` to eliminate the fraction while keeping the system balanced:

`color(red)(4) xx -2 <= color(red)(4) xx (2x - 1)/4 < color(red)(4) xx 2`

`-8 <= cancel(color(red)(4)) xx (2x - 1)/color(red)(cancel(color(black)(4))) < 8`

`-8 <= 2x - 1 < 8`

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

`-8 + color(red)(1) <= 2x - 1 + color(red)(1) < 8 + color(red)(1)`

`-7 <= 2x - 0 < 9`

`-7 <= 2x < 9`

Now, divide each segment by `color(red)(2)` to solve for `x` while keeping the system balanced:

`-7/color(red)(2) <= (2x)/color(red)(2) < 9/color(red)(2)`

`-7/2 <= (color(red)(cancel(color(black)(2)))x)/cancel(color(red)(2)) < 9/2`

`-7/2 <= x < 9/2`

Or

`x >= -7/2`; `x < 9/2`

Or, in interval notation:

`[-7/2, 9/2)`