Question

For what values of x is the expression (x - 4)^2 > 0?

Answer 1

x<4 or x>4

Explanation:

(x - 4)^2 > 0

Take the square root of each side

±sqrt((x - 4)^2) >sqrt( 0)

x-4 > 0 or -(x-4)>0

Solving the first inequality

Add 4 to each side

x>4

Solving the second inequality

Divide each side by -1, remembering to flip the inequality

x-4 <0

Add 4 to each side

x < 4

Answer 2

`x<4\text{ or } x>4`

Explanation:

Solve we have the inequality:

`(x-4)^2>0`

Let's solve it like a normal equation first. So, pretend the inequality is an equal sign:

`(x-4)^2=0`

Solve for x. Zero Product Property:

`x-4=0\text{ or } x-4=-0`

Add 4 to both sides for both equations:

`x=4\text{ or } x=4`

So, our roots are at x=4 and x=4.

Since our original inequality is greater than, this means that our solution will be all values to the left of our first zero and all values to the right of our second zero.

Therefore, our solution is:

`x<4\text{ or } x>4`

Simply put, our x can be anything except for 4 itself.

And we're done!