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Solve the equation.

{:[(2)/(3)p=5],[p=]:}

Solve the equation.\newline23p=5p= \begin{array}{l} \frac{2}{3} p=5 \\ p= \end{array}

Full solution

Q. Solve the equation.\newline23p=5p= \begin{array}{l} \frac{2}{3} p=5 \\ p= \end{array}
  1. Identify Equation: Identify the equation to solve.\newlineWe are given the equation (23)p=5(\frac{2}{3})p = 5, and we need to find the value of pp.
  2. Isolate Variable: Isolate the variable pp. To isolate pp, we need to multiply both sides of the equation by the reciprocal of 23\frac{2}{3}, which is 32\frac{3}{2}. 32×23p=32×5\frac{3}{2} \times \frac{2}{3}p = \frac{3}{2} \times 5
  3. Multiply Left Side: Perform the multiplication on the left side.\newlineThe multiplication on the left side simplifies because (32)×(23)=1(\frac{3}{2}) \times (\frac{2}{3}) = 1. So we have:\newline1×p=(32)×51 \times p = (\frac{3}{2}) \times 5
  4. Multiply Right Side: Perform the multiplication on the right side.\newlineNow we multiply (32)(\frac{3}{2}) by 55:\newlinep=(32)×5p = (\frac{3}{2}) \times 5\newlinep=3×(52)p = 3 \times (\frac{5}{2})\newlinep=3×2.5p = 3 \times 2.5
  5. Calculate Final Value: Calculate the final value of pp.p=3×2.5p = 3 \times 2.5p=7.5p = 7.5