91Ó°ÊÓ

When solving equations, one of the key steps is isolating the variable. This means we aim to get the unknown variable, usually represented by symbols like \(a\), \(x\), or \(y\), by itself on one side of the equation. Let's take a closer look at the exercise provided.We start with the equation: \( \frac{a}{0.4} = -20 \). Our goal here is to solve for \(a\). Right now, \(a\) is divided by 0.4. To isolate \(a\), we need to get rid of the 0.4.To do this, we perform the opposite operation of division, which is multiplication. By multiplying both sides of the equation by 0.4, we can isolate \(a\). Remember, whatever we do to one side of the equation, we must do to the other side to keep it balanced.So, multiplying both sides by 0.4 looks like this:\[ a = -20 \times 0.4 \]Now, \(a\) is by itself on the left side. The next step is to simplify the right side.

Multiplication plays a crucial role when solving equations, especially when we need to isolate a variable. In the given exercise, we needed to isolate \(a\) from \( \frac{a}{0.4} = -20 \). To remove the fraction, we multiply by the denominator's reciprocal.Here's why: When \(a\) is divided by 0.4, it's equivalent to multiplying by the reciprocal of 0.4 (which is 2.5). So, multiplying both sides of the equation \( \frac{a}{0.4} = -20 \) by 0.4 makes the left side just \(a\), since \( \frac{a}{0.4} \times 0.4 = a \).Applying it to our example:This eventually becomes:\[ a = -20 \times 0.4 \]Multiplication steps like these are critical and often used tactics in algebra. The need to keep equations balanced with every mathematical operation you perform is fundamental.

After isolating the variable and setting up the multiplication, the next step is to simplify the expression. Simplification often involves combining like terms or performing basic arithmetic operations.In our example, the equation was reduced to:\[ a = -20 \times 0.4 \]To simplify, we multiply \(-20\) by \(0.4\). It's helpful to remember that multiplying a positive number by a negative number results in a negative number. Here, \(-20\) multiplied by \(0.4\) equals \(-8\).Thus, we find that:\[ a = -8 \]Simplifying is often the easiest step but crucial for arriving at the correct answer. By keeping operations clear and accurate, the variable's value is disclosed correctly. So \(a = -8\) is our solved, simplified answer.