Question

How do you solve `-6\leq \frac { x } { 6} + 3`?

Answer 1

See a solution process below:

Explanation:

First, subtract `color(red)(3)` from each side of the inequality to isolate the `x` term while keeping the inequality balanced:

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

`-9 <= x/6 + 0`

`-9 <= x/6`

Now, multiply each side of the inequality by `color(red)(6)` to solve for `x` while keeping the equation balanced:

`color(red)(6) xx -9 <= color(red)(6) xx x/6`

`-54 <= cancel(color(red)(6)) xx x/color(red)(cancel(color(black)(6)))`

`-54 <= x`

To state the solution in terms of `x` we can reverse or "flip" the entire inequality:

`x >= -54`