Question

Find the sum 1/3(9−6m) + 1/4(12m−8).

a) (9m - 4)/12
b) (3m - 2)/4
c) (7m - 5)/12
d) (5m - 6)/7

Answer 1

When simplifying 1/3(9-6m) + 1/4(12m-8), distribute the fractions into the parentheses, and combine like terms to find the sum. The final simplified form is m + 1, which does not match the provided options, suggesting a possible mistake in the question.

Step-by-step explanation:

The sum of 1/3(9−6m) plus 1/4(12m−8) can be found by first distributing the numbers outside the parentheses and then combining like terms. You can break down the expression step by step:

1. Multiply 1/3 times each term inside the first set of parentheses: 1/3 × 9 = 3 and 1/3 × -6m = -2m.
2. Multiply 1/4 times each term inside the second set of parentheses: 1/4 × 12m = 3m and 1/4 × -8 = -2.
3. After performing the distribution, we have 3 - 2m + 3m - 2.
4. Combine the like terms: -2m and +3m to get +1m, and the constants 3 and -2 to get +1.
5. Thus, the final simplified form is m + 1, which does not match any of the options provided in the question, possibly due to a mistake in the options or an error in the calculation.