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Solve the equation. {:[(1)/(2)=(2)/(3)x],[x=◻]:}

Solve the equation.\newline12=23xx=□ \begin{array}{l} \frac{1}{2}=\frac{2}{3} x \\ x=\square \end{array}

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Full solution

Q. Solve the equation.\newline12=23xx=□ \begin{array}{l} \frac{1}{2}=\frac{2}{3} x \\ x=\square \end{array}
  1. Isolate x: First, we need to isolate xx on one side of the equation.\newlineSo, we'll multiply both sides by the reciprocal of 23\frac{2}{3}, which is 32\frac{3}{2}.\newline(12)×(32)=(23)×x×(32)(\frac{1}{2}) \times (\frac{3}{2}) = (\frac{2}{3}) \times x \times (\frac{3}{2})
  2. Multiply by reciprocal: Now, we simplify both sides.\newline(12)×(32)=34(\frac{1}{2}) \times (\frac{3}{2}) = \frac{3}{4} and (23)×(32)×x(\frac{2}{3}) \times (\frac{3}{2}) \times x simplifies to xx.\newline34=x\frac{3}{4} = x

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