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(7)/(2)(m+12)=(5)/(2)(20+m)

72(m+12)=52(20+m) \frac{7}{2}(m+12)=\frac{5}{2}(20+m)

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Full solution

Q. 72(m+12)=52(20+m) \frac{7}{2}(m+12)=\frac{5}{2}(20+m)
  1. Multiply by 22: Multiply both sides of the equation by 22 to eliminate the denominator.\newline2×72(m+12)=2×52(20+m)2 \times \frac{7}{2}(m+12) = 2 \times \frac{5}{2}(20+m)\newline7(m+12)=5(20+m)7(m+12) = 5(20+m)
  2. Distribute terms: Distribute the 77 and the 55 on both sides of the equation.7m+84=100+5m7m + 84 = 100 + 5m
  3. Subtract 5m5m: Subtract 5m5m from both sides to get the mm terms on one side.\newline7m−5m+84=100+5m−5m7m - 5m + 84 = 100 + 5m - 5m\newline2m+84=1002m + 84 = 100
  4. Isolate mm term: Subtract 8484 from both sides to isolate the mm term.\newline2m+84−84=100−842m + 84 - 84 = 100 - 84\newline2m=162m = 16
  5. Divide by 22: Divide both sides by 22 to solve for mm.2m2=162\frac{2m}{2} = \frac{16}{2}m=8m = 8

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