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49k=8\frac{4}{9}k = 8

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Q. 49k=8\frac{4}{9}k = 8
  1. Identify equation and ask: Identify the equation given and what is being asked.\newlineThe equation given is 49k=8\frac{4}{9}k = 8, and we are asked to find the value of kk.
  2. Isolate variable by multiplying: Isolate the variable kk by multiplying both sides of the equation by the reciprocal of the coefficient of kk. The coefficient of kk is 49\frac{4}{9}, so the reciprocal is 94\frac{9}{4}. Multiply both sides of the equation by 94\frac{9}{4} to isolate kk. \left(\frac{\(9\)}{\(4\)}\right) \times \left(\frac{\(4\)}{\(9\)}k\right) = \left(\frac{\(9\)}{\(4\)}\right) \times \(8
  3. Perform multiplication on both sides: Perform the multiplication on both sides of the equation.\newlineOn the left side, (94)×(49)(\frac{9}{4}) \times (\frac{4}{9}) simplifies to 11, leaving us with kk.\newlineOn the right side, (94)×8(\frac{9}{4}) \times 8 simplifies to 1818.\newlineSo, k=18k = 18.