Question

How do you solve `31- y \geq 8( y - 4)`?

Answer 1

`y<=7`

Explanation:

The key to understanding linear inequalities is not to get confused by the sign, here we have `31-y` is greater than or equal to `8(y-4)`, so we need to find a value for `y` which supports this.

To solve for `y`, it is much like a normal linear equation, the only difference being that if we divide or multiply by a negative number, we switch the side.

So to start with, we must first expand the bracket.

`therefore` `31-y >= 8(y-4)`

`31-y >= 8y-32`

Now we need to rearrange for like terms, therefore we move the `y` over and `32` as we would a linear equation.

`therefore` `63 >=9y` which is the same as `9y<=63`

Now we divide by 9.

`y<=7`

Therefore, if `y` is 7 or less it will hold this inequality true.