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Solve the equation. (1)/(2)=(2)/(3)x x=

Solve the equation.\newline12=23x \frac{1}{2}=\frac{2}{3} x \newlinex= x=

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Full solution

Q. Solve the equation.\newline12=23x \frac{1}{2}=\frac{2}{3} x \newlinex= x=
  1. Isolate x: First, we need to isolate xx on one side of the equation.\newline\(\newline\frac{1}{2} = \frac{2}{3}x\newline\)\newlineTo do this, we can multiply both sides by the reciprocal of 23\frac{2}{3}, which is 32\frac{3}{2}.\newline\(\newline\frac{1}{2} \times \frac{3}{2} = \frac{2}{3}x \times \frac{3}{2}\newline\)
  2. Multiply by reciprocal: Now, we perform the multiplication on both sides.\newline(1×3)/(2×2)=(2×3)/(3×2)x(1 \times 3)/(2 \times 2) = (2 \times 3)/(3 \times 2)x\newlineThis simplifies to:\newline(3)/(4)=x(3)/(4) = x

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