How do you solve (x3)(x4)(x8)0?

1 Answer
Jun 15, 2018

(x3)(x4)(x8)0 when x3 and when 4x8.

Explanation:

For this type of problem, it's probably easiest to draw a table like this:

Original DrawingOriginal Drawing

Our expression is composed of three factors, (x3), (x4), and (x8). These three factors together with their product serve as the top row heading for the table. The most left-hand column shows different possibilities for x, The next column to the right of this shows whether the value of x3 will be negative (-), zero (0), or positive (+) and the last column shows us if the product of the three factors is negative, zero, or positive.

Reading the first row below the heading we can see that when x is less than 3, x3 is negative, x4 is negative, and x8 is negative, so the product of these three factors is also negative, since a negative times a negative times a negative is negative.

Looking at the table, we can see when the product of the factors is less than or equal to zero. This is when

x3, and 4x8.