Final answer:
Only the second original equation (3(x + 6) = 4x + 7) matches with one of the given options, which is option 2) 3x + 18 = 4x + 7, after distributing the 3.
Step-by-step explanation:
To match each equation with an equivalent equation from lesson 7, we must identify which equations are equivalent through algebraic manipulation. It's key to remember that some answer choices might not be used.
- 3x + 6 = 4x + 7: By subtracting 3x from both sides, we get 6 = x + 7. Subtracting 7 from both sides, we arrive at -1 = x. This does not match any of the given options directly.
- 3(x + 6) = 4x + 7: Distributing the 3 inside the parentheses, we get 3x + 18 = 4x + 7. This matches with option 2) 3x + 18 = 4x + 7.
- 4x - 3x = 7 - 6: Simplifying both sides, we get x = 1. We rearrange this to 0 = 3x - 4x - 1, which matches with option 4) 3x - 1 = 4x.
The first and third original equations do not match directly with any of the options presented. Only the second original equation can be matched with one of the given options using algebraic manipulation.