Question

How do you solve `-x / 7 + 4 ≥ 3x`?

Answer 1

`x <= 14/11 " or " x <= 1 3/11`

Explanation:

Given: `-x/7 + 4 >= 3x`

The easiest way to start is to get rid of the fraction by multiplying the whole inequality by `7`:

`-x/cancel(7) *cancel(7)/1+ 4*7 >= 3x*7`

`-x+ 28 >= 21x`

Add `x` to both sides: `" "28 >= 22x`

Divide by `22`: `" "28/22 >= x`

Reduce the fraction: `" "14/11 >= x`

This means `x <= 14/11 " or " x <= 1 3/11`

Answer 2

`x<=14/11`

Explanation:

To get rid of the `7` in the denominator, we can multiply all terms by `7`. This leaves us with

`-x+28>=21x`

Since we did the same thing to both sides, we did not inadvertently change the meaning of this equation.

What we can do next is add `x` to both sides. We get

`22x<=28`

Dividing both sides by `22` gives us

`x<=28/22`

which can be simplified as

`x<=14/11`

Hope this helps!