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To justify each step in solving the equation \( 4x = 7(x - 3) \), let’s fill in the reasons for each statement:

| Statement                   | Reason                                |
|-----------------------------|---------------------------------------|
| 1. \( 4x = 7(x - 3) \)      | Given equation                       |
| 2. \( 4x = 7x - 21 \)       | Distributive property: \(7(x - 3) = 7x - 21\) |
| 3. \( -3x = -21 \)          | Subtraction property of equality: subtract \(7x\) from both sides |
| 4. \( x = 7 \)              | Division property of equality: divide both sides by \(-3\) |

Each step follows logically from the previous one, demonstrating the progression toward isolating \( x \) to find its value.

Would you like more details on each step, or do you have any questions?

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Here are some related questions to consider:

1. How would the solution change if the original equation were \( 4x = 7(x + 3) \) instead?
2. Why is it necessary to use the distributive property in the second step?
3. Can this solution be verified by substituting \( x = 7 \) back into the original equation?
4. What if the equation included additional terms, such as \( 4x + 5 = 7(x - 3) + 10 \)?
5. How would this approach differ if fractions were involved in the equation?

**Tip:** When solving equations, always aim to simplify each side of the equation before isolating the variable. This can make the solution process much clearer and easier to manage.

Justify each step in solving the equation 4x = 7(x - 3) by writing a reason for each statement.

Learn how to solve the linear equation 4x = 7(x - 3) with step-by-step justifications for each operation. This problem covers essential algebraic concepts like the distributive property, subtraction property, and division property of equality, making it ideal for students in Grades 7-9.

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