Solve for x: 3x = 9
(A) 30
(B) 18
(C) 9
(D) 3
The Correct Answer and Explanation is :
The correct answer is:(D) 3
To solve the equation (3x = 9), we need to isolate the variable (x). The goal is to find the value of (x) that satisfies this equation.
Step-by-Step Solution
- Understanding the Equation:
The equation (3x = 9) means that three times some number (x) equals nine. To find (x), we need to eliminate the coefficient (the number multiplying (x)), which in this case is 3. - Isolating (x):
To isolate (x), we can divide both sides of the equation by 3. This step is based on the principle of maintaining equality in an equation, which states that if you do the same operation on both sides of the equation, the two sides remain equal. [
\frac{3x}{3} = \frac{9}{3}
] - Simplifying:
On the left side, dividing (3x) by 3 gives us (x): [
x = \frac{9}{3}
] On the right side, dividing 9 by 3 gives us 3: [
x = 3
] - Conclusion:
Therefore, the solution to the equation (3x = 9) is (x = 3).
Checking the Solution
To ensure our solution is correct, we can substitute (x = 3) back into the original equation:
[
3(3) = 9
]
This simplifies to:
[
9 = 9
]
Since both sides of the equation are equal, our solution is verified.
Final Answer
Thus, the correct answer is (D) 3.
This process demonstrates fundamental algebraic techniques, including the concept of isolating a variable and verifying the solution through substitution. Mastering these skills is essential in solving equations effectively.