I need to write an absolute value equation given the provided products.

Question

I was given the products of an absolute value equation (x=-4 or x=2) and need to write the equation to fit. im not sure where to go for here.

Answer 1

I was given the products of an absolute value equation (x=-4 or x=2) and need to write the equation to fit. i'm not sure where to go for here.

THE SOLUTION (that is, the values of x that make the equation true) are either x=4 or x=2.

The Absolute value operation returns the non-negative magnitude of the expression.

In this case, we would like to find an operation that returns either +N or -N depending on whether x=4 or x=2. Then, when we have |N| it will be just the non-negative value.

So, what operation is that?

Well, (x-3) returns either +1 (when x=4) or -1 (when x=2). Looks like we could use that !!

The equation is:

| x - 3 | = 1

Check:

When x=4, | 4 - 3 | = | +1 | = 1

When x=2, | 2 - 3 | = | -1 | = 1

Interesting note: | 3 - x | also works !!

Answer 2

Normally you would end up with two binomials, set them each equal to zero and solve for x. Here you just need to work backwards.

If you ended up with x = 5 and x = -7

We can work backwards to:

x - 5 = 0 and x + 7 = 0

(x - 5) (x + 7)

x² + 2x - 35