91Ó°ÊÓ

When solving linear equations, one of the first steps is often to isolate the variable. This means getting the variable you want to solve for all by itself on one side of the equation. In the given exercise, the variable we need to solve for is \(a\). The original equation is \( \frac{a}{2} = -9 \). To isolate \(a\), we need to eliminate the fraction. This can be done by multiplying both sides of the equation by the denominator of the fraction (in this case, 2). Once we do that, the equation becomes simpler, and it becomes easier to solve for the variable.

Simplifying equations is a key step in solving them. Once we have isolated the variable, the next step involves simplifying the equation so that we can easily identify the value of the variable. In the given exercise, after isolating the variable \(a\) by multiplying both sides by 2, we are left with the equation \(2 \times \frac{a}{2} = 2 \times (-9)\). This results in \(a = -18\). Here, the process of simplification involves performing basic arithmetic operations. Multiplying \(2\) by \( \frac{a}{2} \) simplifies directly to \(a\), and multiplying \(2\) by \(-9\) gives us \(-18\). Hence, the simplified form of the equation immediately tells us that \(a = -18\).

Multiplication is a fundamental operation in algebra that can help solve equations, especially when dealing with fractions. In the original problem, \( \frac{a}{2} = -9 \), multiplication is used to eliminate the fraction. By multiplying both sides of the equation by \(2\), we get rid of the denominator. This operation is crucial as it transforms the equation into a simpler form and makes it easier to solve. In general, when you multiply terms in an equation by the same number, you maintain the equality, ensuring that the equation's balance is not disturbed. In this problem, we multiplied both sides by \(2\) to get from \( \frac{a}{2} = -9 \) to \(a = -18\). Understanding how and when to apply multiplication can make solving linear equations much more straightforward.