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Solving an equation is like unlocking a mystery. We begin by translating a word problem into a mathematical equation. In our exercise, we identified that a number unknown to us, represented as \( x \), minus eleven equals eighty-five, written as \( x - 11 = 85 \).

Equation solving allows us to find this hidden number by rearranging the equation. The ultimate goal is to have \( x \) isolated on one side while all known values are on the other. This involves performing operations that help us "undo" what has been done to \( x \), such as adding or subtracting numbers to both sides.

A crucial part of solving equations is maintaining balance. Any operation done to one side must be done to the other to keep the equation true. This principle is the bedrock of equation-solving.

Subtraction is one of the basic operations in algebra, often used to isolate a variable. In our exercise, the number eleven was subtracted from \( x \), our unknown number. This operation creates a bridge to understand what happens to \( x \) when we subtract a value from it, leading to the outcome \( 85 \).

Understanding subtraction in algebra is essential. It teaches us to think in terms of "taking away" and helps build a foundation to manipulate equations.

• To undo a subtraction in algebra, we use addition. By adding the same number that was subtracted to both sides of the equation, we return to the original amount.
• In our example, adding \( 11 \) to both sides brought us back to \( x = 96 \).

Being comfortable with both operations allows us to maneuver through complex problems with ease.

Verifying the solution is like double-checking your work to ensure accuracy. It's a simple step but an essential one. Once we solve an equation and find a solution, we should substitute it back into the original equation to confirm it's correct.

In the given example, we checked that \( 96 - 11 = 85 \). Since our outcome was precisely as expected, it confirmed the solution was accurate.

• Verification acts as a safeguard. It protects against computational or conceptual errors.
• This step reinforces understanding by demonstrating the logical flow of algebraic manipulation.

Always remember: verifying is a habit that contributes immensely to success in algebraic problem-solving.