Question

How do you solve `5< 1+ \frac { x } { 7}`?

Answer 1

See the entire solution process below:

Explanation:

First, subtract `color(red)(1)` from each side of the inequality to isolate the `x` term while keeping the inequality balanced:

`-color(red)(1) + 5 < -color(red)(1) + 1 + x/7`

`4 < 0 + x/7`

`4 < x/7`

Now, multiply each side of the inequality by `color(red)(7)` to solve for `x` while keeping the inequality balanced:

`color(red)(7) * 4 < color(red)(7) * x/7`

`28 < cancel(color(red)(7)) * x/color(red)(cancel(color(black)(7)))`

`28 < x`

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

`x > 28`