If 9x=18, what is the value of x?
The Correct Answer and Explanation is:
To solve the equation ( 9x = 18 ), we need to isolate the variable ( x ). Here’s a step-by-step breakdown of the process:
- Understanding the Equation: The equation states that nine times some number ( x ) equals eighteen. This is a linear equation in one variable, which can be solved using basic algebraic techniques.
- Isolating the Variable: To find the value of ( x ), we need to eliminate the coefficient in front of ( x ). The coefficient in this case is 9. We can achieve this by dividing both sides of the equation by 9. [
9x = 18
] Dividing both sides by 9 gives: [
x = \frac{18}{9}
] - Performing the Division: Now, we calculate the right-hand side: [
\frac{18}{9} = 2
] Therefore, ( x = 2 ). - Verifying the Solution: To ensure our solution is correct, we can substitute ( x = 2 ) back into the original equation: [
9(2) = 18
] Simplifying the left side results in: [
18 = 18
] Since both sides of the equation are equal, our solution is verified. - Conclusion: The value of ( x ) that satisfies the equation ( 9x = 18 ) is ( 2 ).
This example illustrates the fundamental principles of algebra, particularly the importance of balancing equations and isolating variables to find solutions. It is crucial for students to master these techniques as they form the foundation for solving more complex algebraic problems. Mastering such simple equations builds confidence and understanding, which are essential for tackling higher-level math concepts in the future.