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When solving equations in algebra, one of the main goals is to find the value of the unknown variable. This process often involves isolating the variable on one side of the equation.
To isolate a variable means to get the variable by itself on one side of the equation.
For example, in the equation given:

\[ x + 58 = 71 \]

The objective is to get \( x \) alone on the left side.
To do this, we perform operations that will eliminate the other terms on the left side.
In this case, we subtract 58 from both sides:

\[ x + 58 - 58 = 71 - 58 \]

This subtraction leaves us with:
\[ x = 13 \]

Now, the variable \( x \) is isolated, and we have found its value.

Next, we simplify the equation to make it easier to solve.
Simplifying involves reducing the equation to its simplest form.
This usually means eliminating any extra terms and combining like terms.
When we isolated the variable in the previous step, we simplified the equation:

\[ x + 58 - 58 = 71 - 58 \]

On the left side of the equation, the \( 58 - 58 \) becomes 0, leaving us with:
\[ x + 0 = x \]

On the right side, we perform the arithmetic subtraction to get:
\[ 71 - 58 = 13 \]

So, the simplified form of the equation is:
\[ x = 13 \]
The equation is now straightforward and easy to understand, which helps in verifying and confirming the solution.

Basic algebra is the foundation of solving equations.
It involves understanding how to manipulate and work with variables and constants.
Key operations include addition, subtraction, multiplication, and division.

In the earlier example, we demonstrated how to solve a basic algebraic equation:
\[ x + 58 = 71 \]

By employing the basic algebraic principle of performing the same operation on both sides of the equation, we can isolate variables and simplify the problem.
Here, subtracting 58 from both sides was the operation chosen to maintain the balance of the equation while solving for \( x \):
\[ x + 58 - 58 = 71 - 58 \]

In basic algebra, preserving balance is crucial; changes must be made to both sides equally.
This consistency ensures that the equation's integrity remains intact while progressing towards the solution.
Whether it’s through addition, subtraction, multiplication, or division, these fundamental algebraic operations provide the necessary tools to solve equations efficiently.