Question

How do you solve and write the following in interval notation: `x/2 + 3 ≤ 1`?

Answer 1

See a solution process below:

Explanation:

This is a standard 2-Step problem:

Step 1: Isolate The Variable: Subtract `color(red)(3)` from each side of the inequality to isolate the `x` term while keeping the inequality balanced:

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

`x/2 + 0 <= -2`

`x/2 <= -2`

Step 2: Multiply or Divide by the Appropriate Term to Solve for the Variable: Multiply each side of the inequality by `color(red)(2)` to solve for `x` while keeping the inequality balanced:

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

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

`x <= -4`

Or, in interval notation:

`(-oo, -4]`