Question
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2. \( 4(\square)=4 \cdot 7+4 \cdot 3 \)

Ask by Robbins Joseph. in the United States
Jan 23,2025

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Tutor-Verified Answer

Answer

\( \square = 10 \)

Solution

To solve the equation \( 4(\square) = 4 \cdot 7 + 4 \cdot 3 \), we will follow these steps: 1. **Calculate the right side of the equation**: - We need to compute \( 4 \cdot 7 \) and \( 4 \cdot 3 \). 2. **Combine the results**: - Add the results of \( 4 \cdot 7 \) and \( 4 \cdot 3 \). 3. **Solve for the unknown**: - Divide both sides of the equation by 4 to isolate the unknown. Let's perform the calculations step by step. ### Step 1: Calculate the right side First, we calculate \( 4 \cdot 7 \) and \( 4 \cdot 3 \): \[ 4 \cdot 7 = 28 \] \[ 4 \cdot 3 = 12 \] ### Step 2: Combine the results Now, we add these two results together: \[ 28 + 12 = 40 \] ### Step 3: Solve for the unknown Now we have the equation: \[ 4(\square) = 40 \] To find \( \square \), we divide both sides by 4: \[ \square = \frac{40}{4} = 10 \] Thus, the solution is: \[ \square = 10 \]

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To solve for the unknown in the equation \( 4(\square)=4 \cdot 7+4 \cdot 3 \), start by simplifying the right side. Multiply and sum: \( 4 \cdot 7 = 28 \) and \( 4 \cdot 3 = 12 \). So, \( 28 + 12 = 40 \). Therefore, the equation becomes \( 4(\square) = 40 \). Dividing both sides by 4 gives us \( \square = 10 \). Once you grasp the distributive property shown here, you can unleash a world of mathematical creativity. This property allows you to simplify expressions across various fields, from algebra to calculus, making problem-solving smoother and more intuitive! So next time you tackle a complex equation, remember, breaking it down can lead to big breakthroughs! To deepen your understanding, consider exploring how the distributive property is the foundation for both polynomial expansions and factoring. You can find real-world applications in areas like finance, where you may need to distribute costs or profits based on multiple factors – that's math in action, right in your day-to-day decisions!

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