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The first step in solving any linear equation is isolating the variable. Isolating the variable means getting the variable (in this case, y) by itself on one side of the equation. This is done using basic arithmetic operations such as addition, subtraction, multiplication, and division. By doing this, we can more easily solve for the value of the variable.

In this specific example, we start with the equation: 1.2y - 4 = 0.2y - 4 . Here, y is the variable, and we want it to be alone on one side of the equation. To do that, follow this approach:

• First, subtract 0.2y from both sides. This ensures that the variable y will be on one side of the equation: 1.2y - 4 - 0.2y = 0.2y - 4 - 0.2y
• Simplify the terms to get: 1.0y - 4 = -4

Now, y is almost isolated, but there is still a constant (-4) on the same side.

Simplifying an equation means performing necessary arithmetic operations to reduce it to its simplest form without altering the equality. Every step should make the equation easier to understand and solve for the variable.

Let's continue from where we left off: 1.0y - 4 = -4
To isolate y completely, we need to eliminate the -4.

• Add 4 to both sides: 1.0y - 4 + 4 = -4 + 4
• This simplifies to: y = 0

After performing these operations, y is completely isolated, and we've simplified the equation to find the solution y = 0.
Note how each arithmetic operation we did maintained the balance of the equation, ensuring that equality holds true.

Always check your solutions to verify they are correct and ensure you didn't make any mistakes during the solving process. This extra step can be crucial, especially in more complicated equations.

To check the solution, substitute the value of y back into the original equation:
Start with: 1.2y - 4 = 0.2y - 4
Substitute y = 0:
1.2(0) - 4 = 0.2(0) - 4
Simplify both sides:

• The left side becomes: 0 - 4 = -4
• The right side becomes: 0 - 4 = -4

Since both sides of the original equation equal -4 when y = 0, this confirms that our solution y = 0 is correct.
Checking solutions is not just about finding out if you have the correct answer, but it also helps reinforce your understanding of the problem and the steps needed to solve similar equations.