Final answer:
Yes, multiplying both sides of the equation 1/3x + 1/2x = 1/6x by 12 is correct and simplifies the equation to 4x + 6x = 2x, which leads to the conclusion that x must be 0 for the original equation to hold true.
Step-by-step explanation:
To solve the equation 1/3x + 1/2x = 1/6x, it is correct to multiply each side by 12, which is a common multiple of the denominators. Multiplying each term by 12 removes fractions, which simplifies the equation substantially.
Multiplying by 12 leads to the following steps:
- Multiply each term by 12, implying that: 12 * (1/3x) + 12 * (1/2x) = 12 * (1/6x).
- This simplifies to: 4x + 6x = 2x.
- After combining like terms, you get: 10x = 2x.
- Solving this results in an equation where 10x and 2x are on the same side, suggesting no solution or an infinite number of solutions if 10x and 2x are equal due to x being 0. Hence, x must be 0 for the original equation to hold true.
Even though we did not use the least common denominator (LCD), the multiplication by 12 still yielded the correct result due to the property that as long as we perform the same operation on both sides of the equals sign, the expression remains an equality.