If 9x - 6(3 - x) = 12 in a linear equation, what is the value of x?

Introduction / Context:
This is a straightforward linear equation in one variable. Such questions appear frequently in aptitude tests to check basic algebra skills, including distribution of multiplication over subtraction and collecting like terms on one side of the equation.

Given Data / Assumptions:

• Equation: 9x - 6(3 - x) = 12
• We assume x is a real number.
• We need to find the numerical value of x.

Concept / Approach:
We use basic algebra:

• Apply distributive property: k(a - b) = ka - kb.
• Combine like terms involving x.
• Isolate x by moving constants to the other side.

The goal is to rewrite the equation into the form kx = constant and then divide both sides by k.

Step-by-Step Solution:
Start with 9x - 6(3 - x) = 12 Distribute -6 over the bracket: -6(3 - x) = -18 + 6x So the equation becomes 9x - 18 + 6x = 12 Combine like terms: 9x + 6x = 15x, so 15x - 18 = 12 Move -18 to the right side: 15x = 12 + 18 = 30 Divide both sides by 15: x = 30 / 15 = 2

Verification / Alternative check:
Substitute x = 2 back into the original equation. Left side is 9(2) - 6(3 - 2) = 18 - 6(1) = 18 - 6 = 12, which matches the right side. This confirms that x = 2 is correct.

Why Other Options Are Wrong:
If x = 4, then 9x - 6(3 - x) becomes 36 - 6(-1) = 42, not 12. If x = 6 or x = 9, the left side becomes much larger than 12. If x = 0, the left side is -18, which also does not match 12. Hence these options do not satisfy the equation.

Common Pitfalls:
A common mistake is to distribute the minus sign incorrectly, writing -6(3 - x) as -18 - 6x instead of -18 + 6x. Another error is not carefully combining 9x and 6x. Careful handling of signs at each step avoids these issues.

Final Answer:
The value of x that satisfies the equation is 2.