Solving the Equation 9x - 9 99: A Comprehensive Guide to Basic Algebra

Introduction

Algebra is a fundamental branch of mathematics that involves solving equations using various techniques. One classic problem often used to teach basic algebra is the equation 9x - 9 99. Let's dive into a step-by-step explanation of how to solve this problem and explore some related concepts.

Solving the Equation 9x - 9 99

Solution Method 1

To solve the equation 9x - 9 99, we follow these steps:

Isolate the term containing the variable (x) by adding 9 to both sides: Perform the addition: Divide both sides by the coefficient of x: Calculate the final value:

Example:

9x - 9  99
9x - 9   9  99   9  # Adding 9 to both sides
9x  108
x  108 / 9  # Dividing both sides by 9
x  12  # Calculating the value

Therefore, the solution is x 12.

Solution Method 2

We can also solve the equation by dividing directly:

Divide both sides of the equation by 9: Perform the division: Determine the value of x:

Example:

9x - 9  99
(9x - 9) / 9  99 / 9  # Dividing both sides by 9
x - 1  11  # Simplifying the left side
x  11   1  # Adding 1 to both sides
x  12  # Final value

Again, the solution is x 12.

Exploring the Problem in Other Bases

The equation 9x - 9 99 can also be explored in different number bases. For instance, in base 11, the numbers are represented differently:

Base 11 Representation

911 9 9911 9 * 11 9 10810

Therefore, the equation becomes:

911x - 911 9911

Simplify it:

911x - 911 10810

Let's solve it:

911x - 911  10810
911x  10810   911
911x  10810   9  # In base 10
x  11010 / 9
x  12.222210  # Reciprocating in base 11

This shows that the value of x in base 11 is approximately 12.2222.

Conclusion

This illustrative problem demonstrates the fundamental principles of algebra, including solving equations and understanding number representation in different bases. Whether in base 10 or other bases, the key is to isolate the variable and solve the problem systematically.

For more algebraic challenging problems and comprehensive resources, consider exploring related concepts and exercises in algebra textbooks or online educational platforms.