Question

How do you solve `-9\leq \frac { 3x + 17} { 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 -9 <= color(red)(4) xx (3x + 17)/4 < color(red)(4) xx 2`

`-36 <= cancel(color(red)(4)) xx (3x + 17)/color(red)(cancel(color(black)(4))) < 8`

`-36 <= 3x + 17 < 8`

Next, subtract `color(red)(17)` from each segment to isolate the `x` term while keeping the system balanced:

`-36 - color(red)(17) <= 3x + 17 - color(red)(17) < 8 - color(red)(17)`

`-53 <= 3x + 0 < -9`

`-53 <= 3x < -9`

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

`-53/color(red)(3) <= (3x)/color(red)(3) < -9/color(red)(3)`

`-53/3 <= (color(red)(cancel(color(black)(3)))x)/cancel(color(red)(3)) < -3`

`-53/3 <= x < -3`

Or

`x >= -53/3` and `x < -3`

Or, in interval notation:

`[-53/3, -3)`