91Ó°ÊÓ

To solve an equation, the goal is to find the value of the variable that makes the equation true. In the given equation, \(-1.3a = -10.4\), our task is to determine the value of \(a\). This involves using various algebraic techniques to manipulate the equation. The technique we will use here is the Multiplication Principle. By applying these methods step-by-step, we can solve for \(a\) efficiently.
The process often involves:

• Understanding the structure and terms of the equation.
• Applying algebraic principles such as the Multiplication Principle.
• Isolating the variable to find its value.
• Checking the solution to ensure it satisfies the original equation.

Next, we will break down each of these steps in detail.

Isolating the variable is one of the key steps in solving an equation. In our equation, \(-1.3a = -10.4\), we need to isolate \(a\). This means getting \(a\) by itself on one side of the equation. To do this, we use the Multiplication Principle.
In this context, the Multiplication Principle lets us divide both sides of the equation by the same number, as long as it is not zero. Here, we divide both sides by \(-1.3\):
\(\frac{-10.4}{-1.3} = a\)
The negative signs on both the numerator and the denominator cancel each other out, making the operation straightforward:
\(a = 8\)
By dividing both sides by the coefficient of \(a\), we have successfully isolated \(a\). It's important to always ensure we are using valid algebraic manipulations to maintain the equality.

After isolating the variable and solving for \(a\), it is crucial to check the solution. This step ensures that our solution actually satisfies the original equation. To do this, we substitute the value of \(a\) back into the original equation.
In our case:
\(-1.3 \times 8 = -10.4\)
Calculate the left-hand side:
\-10.4 = -10.4\
Since both sides of the equation are equal, our solution \(a = 8\) is verified to be correct. This confirmation step guards against any arithmetic or algebra mistakes and ensures our solution is accurate.