Question

How do you solve `2<=4-3x<7`?

Answer 1

See the entire solution process below:

Explanation:

First, subtract `color(red)(4)` from each segment of the inequality to isolate the `x` term while keeping the system of inequalities balanced:

`2 - color(red)(4) <= 4 - 3x - color(red)(4) < 7 - color(red)(4)`

`-2 <= 4 - color(red)(4) - 3x < 3`

`-2 <= 0 - 3x < 3`

`-2 <= -3x < 3`

Now, divide each segment of the inequality system by `color(blue)(-3)` to solve for `x` while keeping the system of inequalities balanced. However, remember, when dividing or multiplying an inequality by a negative number you must reverse the inequality terms:

`(-2)/color(blue)(-3) color(red)(>=) (-3x)/color(blue)(-3) color(red)(>) 3/color(blue)(-3)`

`2/3 color(red)(>=) (color(blue)(cancel(color(black)(-3)))x)/cancel(color(blue)(-3)) color(red)(>) -1`

`2/3 color(red)(>=) x color(red)(>) -1`