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Solving an equation is like unraveling a mystery. You are given clues in the form of numbers and operations, and your goal is to find the unknown variable's value. The given equation, \(6a + 3 = 3\), is a linear equation. Linear equations are equations that form a straight line when graphed, and they generally have variables with exponents of one.

The first important step in solving equations is ensuring both sides of the equation remain balanced. It’s like a scale: anything you do on one side, you must do the same on the other to keep it balanced.

To simplify and solve, follow these general steps:

• Identify how to isolate the variable terms.
• Use arithmetic operations like addition, subtraction, multiplication, or division.
• Simplify both sides to find an answer.

When isolating variables, you’re essentially peeling back layers to reveal the core, which is the variable's value. Think about this process like peeling an onion or unwrapping a present. In the equation \(6a + 3 = 3\), the goal is to get "\(a\)" by itself on one side of the equation.

Start by looking at what is added or subtracted to the variable. In this example, a constant "\(+3\)" is present. To isolate \(a\), you need to remove this "+3" from the side with \(a\).

• Subtract 3 from both sides to keep the equation balanced: \(6a + 3 - 3 = 3 - 3\).
• Once simplified, this results in \(6a = 0\).

Now the only layer is the multiplication by 6. Divide both sides by 6 to completely isolate \(a\), giving you:\(a = 0\).

Once isolated, you've solved for your variable! This approach is essential for solving any linear equation.

Checking your solution is like double-checking your work in a puzzle. After determining \(a = 0\), substitute it back into the original equation \(6a + 3 = 3\) to verify your answer. This step ensures your solution is correct and that no mistakes were made during calculations.

Inserting \(0\) in place of \(a\), the equation becomes \(6(0) + 3 = 3\). Simplify the expression:

• Calculate \(6 \times 0\) which gives \(0\).
• Add \(0 + 3\) to get \(3\).

The left side \(3\) matches the right side \(3\), confirming that \(a = 0\) is indeed the correct solution.

This practice of checking ensures accuracy and reinforces understanding of each step in solving equations. It’s a great habit to form whenever working with equations.