91Ó°ÊÓ

Understanding equation simplification is vital for solving linear equations. This technique transforms complex equations into simpler forms. In the exercise \( -4y + 15 = 15 \), simplification begins with eliminating like terms or constants on both sides. Here, the constant 15 is present on both sides of the equation.

To simplify, subtract 15 from both sides: \[ -4y + 15 - 15 = 15 - 15 \] which results in the much simpler equation: \[ -4y = 0 \]. Simplification doesn’t change the solution to the equation; it just makes it easier to find that solution. Always aim to simplify equations to their barest form before trying to solve for the unknown variable.

Once you've simplified the equation, the next step is isolating the variable, which is y in our case. Isolating the variable means rearranging the equation so the variable is by itself on one side of the equation, and everything else is on the other side.

For the simplified equation \( -4y = 0 \), the goal is to get y on its own. To isolate y, divide both sides of the equation by -4, the coefficient of y: \[ y = \frac{0}{-4} \]. This simplification yields the straightforward solution \( y = 0 \). Dividing by the coefficient is essential whenever the variable you are solving for is multiplied by a number. It's like unraveling a knot—the right operation provides a clear path to the answer.

Verifying your solution is an often overlooked but critical step in solving equations. It ensures the answer is correct by plugging it back into the original equation to see if it satisfies the equation.

For the given problem, substitute the found value of y into the original equation \( -4y + 15 \): \[ -4(0) + 15 = 15 \]. Since \( -4 \times 0 \)= 0, you're left with 15 = 15, which confirms our solution is correct. It's like double-checking your work in real life—taking a moment to ensure everything adds up perfectly. Solution verification is not to be skipped; think of it as the seal of approval on your answer.