Final answer:
To solve the equation 4/7m = 18 - 2/7m, we first multiply all terms by 7 to eliminate the fractions, combine like terms, and then solve for m, finding that m = 21. However, this solution does not match the provided options.
Step-by-step explanation:
To solve the equation 4/7m = 18 - 2/7m, we will first eliminate the fractions by multiplying every term by 7 (the least common denominator of the fractions involved).
Step 1: 7 * (4/7m) = 7 * 18 - 7 * (2/7m)
4m = 126 - 2m
Now, we add 2m to both sides to get all the m terms on one side:
Step 2: 4m + 2m = 126
6m = 126
Then, we divide both sides by 6 to solve for m:
Step 3: m = 126 / 6
m = 21
So, the value of m that satisfies the equation is 21. However, looking at the provided options, none of them matches our solution. This may indicate that the solution needs to be verified or there has been a typographical issue with the options provided.