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When solving linear equations, one crucial step is moving all terms involving the variable (in this case, x) to one side of the equation. This simplifies the equation and makes it easier to solve for the variable. Consider the equation: 6x - 4 = 7x.
To isolate the variable, we need to move the 6x term to the right side. We do this by subtracting 6x from both sides of the equation: 6x - 4 - 6x = 7x - 6x.
This subtraction cancels out 6x on the left side, making it simpler to solve. After simplification, we get: -4 = x.
By moving all terms involving x to one side, we effectively isolate the variable, setting up an equation that’s straightforward to solve. Always remember, whatever operation you perform on one side, you must do the same on the other to maintain the equality.

The subtraction method is a fundamental technique in algebra used to isolate the variable in an equation. In the initial equation: 6x - 4 = 7x, we can use subtraction to rearrange terms.
First, identify which term involving the variable should be moved. Here, subtract 6x from both sides:
6x - 4 - 6x = 7x - 6x.
By performing the subtraction, the 6x terms cancel each other out on the left side:
-4 = x.
Now, -4 equals x, and our equation is simplified to a much more manageable form.
It’s essential to perform the same operation on both sides to maintain balance.
Whether you are subtracting, adding, multiplying, or dividing, always apply the operation equally to both sides of the equation to keep it correct.

Once you have solved the equation and found a value for the variable, it is crucial to verify the solution. Verification ensures that the solution is accurate and satisfies the original equation. In our example, we found that x = -4.
To verify, substitute x = -4 back into the original equation: 6(-4) - 4 = 7(-4).
Perform the multiplication:
-24 - 4 = -28.
Simplify both sides: -24 - 4 equals -28.
Since both sides of the original equation equal -28 when x = -4 is substituted, our solution is verified. This step confirms that we have solved the equation correctly.
Always verify your solutions to avoid errors and ensure that the solution fits the original problem.