When solving an equation with one variable, the key rule is to isolate the variable on one side of the equal sign and move all the numbers to the other side.

To do this, you transfer terms from one side to the other by changing their signs: if a term is added on one side, it becomes subtracted on the other, and if it is subtracted, it becomes added.

This process helps simplify the equation and makes it easier to solve for the unknown variable.

For example, if you have x + 3 = 7, you move the +3 to the other side as -3, resulting in x = 7 – 3. This method ensures a clear and systematic way to find the value of the variable.

2x – 5 = 10

2x= 10 + 5

2x = 15

x = 15/2

x = 7.5

You can add together variables by combining their values, such as x + y, which results in the sum of the two variables. You can also subtract numbers directly, like 5 – 3, which equals 2. However, you cannot subtract a number from a variable or vice versa without additional context, because variables represent unknown values.

For example, expressions like x – 3 or 5 – y are valid symbolic expressions but cannot be simplified further unless the variable values are known. Therefore, adding variables or subtracting numbers is straightforward, but combining numbers directly with variables requires careful handling.

Let’s solve the equation step by step:

Given:
2x + 3 + 6x = 3x – 3 – 2x

Step 1: Arrange all variables on one side and constants on the other side.
Move the terms with x on the right side to the left by subtracting 3x and adding 2x to both sides:
2x + 6x – 3x + 2x + 3 = -3

Step 2: Combine like terms on the left side.
(2x + 6x – 3x + 2x) + 3 = -3
(7x) + 3 = -3

Step 3: Move constants to the right side.
7x = -3 – 3
7x = -6

Step 4: Solve for x by dividing both sides by 7.
x = -6 / 7

Final answer:
x = -6/7

CONCLUSION

When you know the rules, every equation can be solved because these rules provide a systematic way to manipulate and simplify the equation. The rules include operations like addition, subtraction, multiplication, division, and the properties of equality, which allow you to isolate the variable you are trying to find. By applying these rules step-by-step, you transform the equation into a simpler form until you reach a solution. Understanding these rules also helps you recognize different types of equations and the best methods to solve them, ensuring that no equation is unsolvable if approached correctly.