Use the Zero Product Property to find the value of x that makes the following statement true: 2 x (x-3) = 0.

The value that makes the statement true is x = ___

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
3 days ago

To use the Zero Product Property, we start with the equation:

\[ 2x(x - 3) = 0 \]

According to the Zero Product Property, if the product of two factors is zero, at least one of the factors must be zero. In this case, we can see that the factors are \( 2x \) and \( (x - 3) \).

We set each factor equal to zero:

1. \( 2x = 0 \)

Dividing both sides by 2 gives:

\[ x = 0 \]

2. \( x - 3 = 0 \)

Adding 3 to both sides gives:

\[ x = 3 \]

Thus, the solutions are:

\[ x = 0 \] and \( x = 3 \]

The values that make the statement true are \( x = 0 \) and \( x = 3 \). You can fill in the blank with either value based on your preference or context provided.

For example, the value that makes the statement true is \( x = 0 \) or \( x = 3 \).