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In solving linear equations, one of the most critical steps is isolating the variable. This means getting the variable by itself on one side of the equation. To achieve this, you need to undo any addition, subtraction, multiplication, or division that is affecting the variable.

Let's use our example equation: \[ 10t = -36 \] Here, the variable 't' is multiplied by 10. To isolate 't', you need to do the opposite of multiplication, which is division. Divide both sides of the equation by 10.

\[ \frac{10t}{10} = \frac{-36}{10} \] This simplifies to: \[ t = -3.6 \] Always make sure to perform the same operation on both sides to keep the equation balanced. This ensures that the equality remains true.

Once you isolate the variable and find its value, the next step is to verify the solution. Verification ensures that the solution you found is correct and satisfies the original equation.

To verify, substitute the solution back into the original equation and check if both sides are equal. Let's proceed with our example:

Start with the original equation: \[ 10t = -36 \] Substitute the solution \[ t = -3.6 \]: \[ 10(-3.6) = -36 \] Simplify the left side: \[ -36 = -36 \] Since both sides match, the solution is verified. This is a crucial step as it confirms the correctness of your solution and ensures there were no calculation errors.

Simple algebraic equations typically involve one variable and basic arithmetic operations such as addition, subtraction, multiplication, and division. The main goal is to determine the value of the variable that makes the equation true.

In our example \[ 10t = -36 \], this is a linear equation because the variable 't' is raised to the power of 1. Solving these types of equations usually involves straightforward steps like:

• Combining like terms


• Isolating the variable


• Performing inverse operations (like dividing when multiplied)


• Checking the solution through substitution

These steps are foundational for understanding more complex algebraic equations. Mastering these will build a strong base for further mathematics learning.