Question

If 3(x−4) = x 4, then x = 8. Put responses in the correct input to answer the question.

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Statement Reason 1: 3(x−4) = x 4
Statement Reason 2: 3x−12 = x 4
Statement Reason 3: 3x−12 12 = x 4 12
Statement Reason 4: 3x−x = x 16−x

Answer 1

To solve the equation 3(x−4) = x + 4, we first distribute 3 inside the parenthesis, then add 12 to both sides, simplify the equation, combine like terms, and then divide by 2 to solve for x, getting x = 8.

Step-by-step explanation:

The equation provided, 3(x−4) = x + 4, if simplified correctly should lead us to find the value of x.

1. Statement: 3(x−4) = x + 4 (Given equation).
2. Reason: 3x−12 = x + 4 (Distribute 3 to both terms inside the parenthesis).
3. Statement: 3x−12 + 12 = x + 4 + 12 (Add 12 to both sides to isolate the x terms on one side).
4. Reason: 3x = x + 16 (Simplify the equation).
5. Statement: 3x − x = 16 (Subtract x from both sides).
6. Reason: 2x = 16 (Combine like terms).
7. Statement: x = 8 (Divide by 2 to solve for x).

By following these steps, we clearly see that the solution x = 8 satisfies the initial equation, which can also be verified by substitution.