Question

How do you solve `1< 3- 5x \leq 6`?

Answer 1

See a solution process below:

Explanation:

Step 1) Subtract `color(red)(3)` from each segment of the system of inequalities to isolate the `x` term while keeping the system balanced:

`-color(red)(3) + 1 < -color(red)(3) + 3 - 5x <= -color(red)(3) + 6`

`-2 < 0 - 5x <= 3`

`-2 < -5x <= 3`

Step 2) Divide each segment by `color(blue)(-5)` to solve for `x` while keeping the system balanced. However, because we are multiplying or dividing inequalities by a negative number we must reverse the inequality operators:

`(-2)/color(blue)(-5) color(red)(>) (-5x)/color(blue)(-5) color(red)(>=) 3/color(blue)(-5)`

`2/5 color(red)(>) (color(blue)(cancel(color(black)(-5)))x)/cancel(color(blue)(-5)) color(red)(>=) -3/5`

`2/5 color(red)(>) x color(red)(>=) -3/5`

Or

`x >= -3/5` and `x < 2/5`

Or, in interval notation:

`[-3/5, 2/5)`