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One of the first steps in solving any linear equation is isolating the variable. This means getting the variable by itself on one side of the equation. In our exercise, the original equation is given as: \( 3a=-15 \). To isolate \( a \), we need to remove the coefficient (in this case, 3) that is attached to it.
To do this, we can divide both sides of the equation by 3. This operation looks like this:
\(\frac{3a}{3} = \frac{-15}{3} \).
When we divide, the equation simplifies to: \( a = -5 \).
This step is crucial in solving linear equations because it allows you to clearly see the value of the variable in question.
Remember, the goal of isolating the variable is to rewrite the equation in a simpler form that directly gives us the answer. Keep practicing, and you’ll find it becomes second nature!

After isolating the variable and finding its value, the next important step is to check the solution. This helps confirm that the solution you found is indeed correct. To do this, substitute the value of the variable back into the original equation and see if both sides are equal.
For our example, we found that \( a = -5 \). We substitute \( a \) with -5 in the original equation:
\( 3(-5) = -15 \).
When we perform the multiplication, we get \( -15 = -15 \). Since both sides of the equation are equal, this means our solution is correct.
Checking your solutions can prevent many common mistakes and ensure that you understand the problem-solving process fully. It is a great habit to develop in all areas of math.

Understanding basic algebra is fundamental in solving equations and many other types of mathematical problems. Algebra involves working with variables, constants, and coefficients to find unknown values. In this exercise, you dealt with a simple linear equation: \( 3a = -15 \).
Here are some key concepts in basic algebra:

• Variables: Symbols (like \( a \)) that represent unknown values.
• Constants: Specific known values (like -15).
• Coefficients: Numbers that multiply the variable (like 3).

By understanding how to manipulate these components, such as isolating the variable and performing operations on both sides of the equation, you can solve for the unknowns.
Basic algebra acts as a building block for more complex math, making it essential to master these concepts early on. Practice regularly and keep challenging yourself with more equations to strengthen your algebra skills!