Final answer:
The equivalent equation to y - 7 = 14(8x + 12) is y = 14(8x + 12) + 7, which corresponds to option 1). This is solved by adding 7 to both sides of the original equation.
Step-by-step explanation:
The student asked which equation is equivalent to y - 7 = 14(8x + 12). To determine the equivalent equation, we need to solve for y. We add 7 to both sides of the equation to isolate y, which gives us:
y = 14(8x + 12) + 7
Therefore, the equivalent equation is option 1) y = 14(8x + 12) + 7. Options 2) and 3) have also redistributed the 14 to the terms in the parentheses, but option 2) incorrectly subtracts 7 instead of adding it, and option 3) is the same as option 1). Option 4) has the term -14(12) which is not equivalent to the original equation.
This example demonstrates solving linear equations by applying basic algebraic principles, specifically the distributive property and inverse operations to isolate the variable.