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When solving equations, the primary goal is to find the value of the unknown variable that makes the equation true. Here, we're dealing with an absolute value equation. An absolute value equation involves expressions within the absolute value bars, like \(|y|\), which means the distance of y from zero on a number line. In this particular case:1. **Identify the equation**: Start with \(\frac{3 |y|}{2} = 6\).2. **Clear fractions or decimals**: Multiply every term by the denominator if there's a fraction, which simplifies solving. Here, we multiply both sides by 2 to eliminate the fraction.3. **Simplify**: By multiplying by 2, the equation becomes \(3|y| = 12\). This transformation makes it simpler to work with.4. **Isolate the variable**: Eventually, most equations can be reduced to a simpler form through strategic operations until the variable is isolated, leading to solutions.

Isolating the variable is a crucial step in solving any equation. It involves rearranging the equation so that the variable (e.g., |y| in this case) stands alone on one side. Here's how it happens in the context of absolute value:- After clearing any fractions or coefficients as we did by eliminating the denominator, focus on making \(|y|\) the subject of the equation.- With our equation as \(3|y| = 12\), the next step is to get |y| alone. We divide both sides by 3, thus simplifying our equation to \(|y| = 4\).- At this point, the equation clearly shows that the absolute value of y is 4. This highlights how isolating the variable simplifies understanding what the equation represents before solving it.

Multiplication plays a pivotal role in solving equations, especially when eliminating denominators or coefficients. Here's how it unfolds in our absolute value equation:- **Eliminating a fraction**: We initially multiplied both sides of \(\frac{3|y|}{2} = 6\) by 2. This step cancels the denominator (2) and converts the equation into an equivalent format without fractions, \(3|y| = 12\).

• This operation maintains equality because if two sides of an equation are equal, multiplying both sides by the same number preserves that equality.

- **Dividing to simplify**: Following that, we use multiplication properties in reverse by dividing to isolate |y|, transforming \(3|y| = 12\) into \(|y| = 4\).- **Multiplication effects**: These operations demonstrate how multiplication (or division) can remove obstacles of solving equations, such as fractions or unnecessary coefficients, setting the stage for isolating and solving for unknowns like y.