Question

How do you solve `y^2-4>0` using a sign chart?

Answer 1

Either `y < -2` or `y > 2`

Explanation:

As `y^2-4>0`, factorizing we have `(y+2)(y-2)>0`

From this we know that the product `(y+2)(y-2)` is positive. It is apparent that sign of binomials `(y+2)` and `y-2` will change around the values `-2` and `2` respectively. In sign chart we divide the real number line using these values, i.e. below `-2`, between `-2` and `2` and above `2` and see how the sign of `y^2-4` changes.

Sign Chart

`color(white)(XXXXXXXXXXX)-2color(white)(XXXXX)2`

`(y+2)color(white)(XXX)-ive color(white)(XXXX)+ive color(white)(XXXX)+ive`

`(y-2)color(white)(XXX)-ive color(white)(XXXX)-ive color(white)(XXXX)+ive`

`(y^2-4)color(white)(XXX)+ive color(white)(XXX)-ive color(white)(XXXX)+ive`

It is observed that `y^2-4 > 0` when either `y < -2` or `y > 2`, which is the solution for the inequality.