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3(m+2)9=5(m−4)10\frac{3(m+2)}{9}=\frac{5(m-4)}{10}\newlineIn the equation above, what is the value of \newlinemm?\newlineA. 66\newlineB. 1111\newlineC. 1616\newlineD. 2828

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Q. 3(m+2)9=5(m−4)10\frac{3(m+2)}{9}=\frac{5(m-4)}{10}\newlineIn the equation above, what is the value of \newlinemm?\newlineA. 66\newlineB. 1111\newlineC. 1616\newlineD. 2828
  1. Simplify Fractions: First, we need to simplify the equation (3(m+2))/9=(5(m−4))/10(3(m+2))/9 = (5(m-4))/10. We can start by reducing the fractions on both sides of the equation. The left side has a denominator of 99, which is divisible by 33, and the right side has a denominator of 1010, which is divisible by 55.
  2. Divide and Simplify: Simplify the left side by dividing both the numerator and the denominator by 33. This gives us (m+2)/3(m+2)/3.
  3. Eliminate Fractions: Simplify the right side by dividing both the numerator and the denominator by 55. This gives us (m−4)/2(m-4)/2.
  4. Find Common Denominator: Now we have a simplified equation: (m+2)/3=(m−4)/2(m+2)/3 = (m-4)/2. To solve for mm, we need to get rid of the fractions by finding a common denominator and then cross-multiplying.
  5. Cross-Multiply: The common denominator for 33 and 22 is 66. Multiply both sides of the equation by 66 to eliminate the fractions: 6×(m+2)3=6×(m−4)26 \times \frac{(m+2)}{3} = 6 \times \frac{(m-4)}{2}.
  6. Distribute and Simplify: On the left side, the 66 cancels with the 33 in the denominator, leaving us with 2(m+2)2(m+2). On the right side, the 66 cancels with the 22 in the denominator, leaving us with 3(m−4)3(m-4).
  7. Isolate Variable: Now we have a new equation without fractions: 2(m+2)=3(m−4)2(m+2) = 3(m-4). Distribute the 22 on the left side and the 33 on the right side to get 2m+4=3m−122m + 4 = 3m - 12.
  8. Solve for mm: To isolate mm, we need to get all the mm terms on one side and the constant terms on the other. Subtract 2m2m from both sides to get 4=m−124 = m - 12.
  9. Solve for m: To isolate mm, we need to get all the mm terms on one side and the constant terms on the other. Subtract 2m2m from both sides to get 4=m−124 = m - 12.Now, add 1212 to both sides to solve for mm: 4+12=m4 + 12 = m. This gives us m=16m = 16.

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