To solve the equation \( 41.4 = 3.6(x + 4.5) \) using the distributive property, follow these steps:
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Distribute the \( 3.6 \) to both terms inside the parentheses: \[ 41.4 = 3.6 \cdot x + 3.6 \cdot 4.5 \] Calculate \( 3.6 \cdot 4.5 \): \[ 3.6 \cdot 4.5 = 16.2 \] So the equation now becomes: \[ 41.4 = 3.6x + 16.2 \]
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Isolate the term with \( x \) by subtracting \( 16.2 \) from both sides: \[ 41.4 - 16.2 = 3.6x \] Calculate the left side: \[ 41.4 - 16.2 = 25.2 \] Now the equation is: \[ 25.2 = 3.6x \]
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Solve for \( x \) by dividing both sides by \( 3.6 \): \[ x = \frac{25.2}{3.6} \] Calculate the division: \[ x = 7 \]
Thus, the solution to the equation is: \[ \boxed{7} \]
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