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The distributive property is a powerful tool in algebra that helps us simplify expressions and solve equations efficiently. It's used when you have a number outside a set of parentheses that needs to be distributed across the terms inside the parentheses. For the equation \( 5(3y - 2) = 16y \), you need to apply the distributive property by multiplying \(5\) with each term inside the parentheses.
Here’s how you do it:

• Multiply \(5 \times 3y\) to get \(15y\).
• Multiply \(5 \times (-2)\) to get \(-10\).

The result is \( 15y - 10 \). It transforms the equation into a simpler form without parentheses, making it easier to handle. Using this property keeps your calculations straightforward and accurate, especially in equations where multiple terms are compounded together. Once the distributive step is completed, the equation becomes easier to solve, paving the way to isolate the variable.

Isolating the variable is the crucial step in solving equations. The goal is to get the variable, in this case, \( y \), on one side of the equation so you can easily see what it equals. From our equation \( 15y - 10 = 16y \), we want to move all terms involving \( y \) to one side.Start by eliminating \( 15y \) from the left side of the equation. We do this by subtracting \( 15y \) from both sides. Here's what it looks like:

• Subtracting \( 15y \) from \( 15y - 10 \) gives you \(-10\).
• Subtracting \( 15y \) from \( 16y \) leaves you with \( y \).

This manipulation simplifies our equation to \( -10 = y \). As you can see, the variable \( y \) is now isolated, making it clear that \( y = -10 \). Properly isolating the variable ensures that you arrive at the correct solution without confusion.

Verification is a critical step to ensure that the solution you've found is indeed correct. After isolating the variable and determining that \( y = -10 \), we substitute it back into the original equation to check our work.The original equation is \( 5(3y - 2) = 16y \). Substitute \( y = -10 \) into the equation:

• The left side becomes \( 5(3(-10) - 2) = 5(-32) \), which simplifies to \(-160\).
• The right side is \( 16(-10) \), which also simplifies to \(-160\).

Since both sides equal \(-160\), the solution \( y = -10 \) is verified as correct. Verification is like double-checking your work; it provides reassurance that your solution accurately satisfies the original equation. It’s a safety net to catch potential mistakes and ensures you have a reliable result to present.