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Use the zero product property to find the value of c that makes the following statement true: 2⋅(x - 3) = 0Question
Use the Zero Product Property to find the value of x that makes the following statement true: 2⋅(x−3)=0
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GPT-4o mini
To solve the equation \( 2 \cdot (x - 3) = 0 \) using the Zero Product Property, we follow these steps:
1. **Identify the product**: The equation is already in the form of a product equal to zero. The product is \( 2 \) and \( (x - 3) \).
2. **Set the product to zero**: According to the Zero Product Property, if the product of two factors is zero, then at least one of the factors must be zero. Since \( 2 \) is a constant and not equal to zero, we focus on the other factor:
\[
(x - 3) = 0
\]
3. **Solve for \( x \)**: Now, we can solve the equation \( x - 3 = 0 \):
\[
x - 3 = 0 \implies x = 3
\]
Thus, the value of \( x \) that makes the statement true is \( \boxed{3} \).
1. **Identify the product**: The equation is already in the form of a product equal to zero. The product is \( 2 \) and \( (x - 3) \).
2. **Set the product to zero**: According to the Zero Product Property, if the product of two factors is zero, then at least one of the factors must be zero. Since \( 2 \) is a constant and not equal to zero, we focus on the other factor:
\[
(x - 3) = 0
\]
3. **Solve for \( x \)**: Now, we can solve the equation \( x - 3 = 0 \):
\[
x - 3 = 0 \implies x = 3
\]
Thus, the value of \( x \) that makes the statement true is \( \boxed{3} \).
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