Ответ:

[tex]23.4 \div (x - 13.5) = \frac{2}{3} [/tex]

[tex]\color{red}{x - 13.5 = 0 } \\ \color{red}{x = 13.5}[/tex]

[tex]23.4 \div (x - 13.5) = \frac{2}{3} .x≠13.5[/tex]

[tex] \frac{117}{5} \div (x - \frac{27}{2} ) = \frac{2}{3} [/tex]

[tex] \frac{117}{5} \div \frac{x}{1} - \frac{27}{2} = \frac{2}{3} [/tex]

[tex] \frac{117}{5} \div \frac{2x}{2 \times 1} - \frac{27}{2} = \frac{2}{3} [/tex]

[tex] \frac{117}{5} \div \frac{2x}{2} - \frac{27}{2} = \frac{2}{3} [/tex]

[tex] \frac{117}{5} \div \frac{2x - 27}{2} = \frac{2}{3} [/tex]

[tex] \frac{115}{5} \times \frac{2}{2x - 27} = \frac{2}{3} [/tex]

[tex] \frac{117 \times 2}{5(2x - 27)} = \frac{2}{3} [/tex]

[tex] \frac{234}{5(2x - 27)} = \frac{2}{3} [/tex]

[tex]234 \times 3 = 2 \times 5(2x - 27)[/tex]

[tex]702 = 10(2x - 27)[/tex]

[tex]702 = 10 \times 2x - 10 \times 27[/tex]

[tex]702 = 20x - 270[/tex]

[tex] - 20x = - 270 - 702[/tex]

[tex] - 20x = - 972[/tex]

[tex] - 20x \div ( - 20) = - 972 \div ( - 20)[/tex]

[tex]x = \frac{972}{20} [/tex]

сокращаем на общий делитель 4:

[tex]x = \frac{243}{5} .x≠13.5[/tex]

[tex]x = \frac{243}{5} .x≠ \frac{27}{2} [/tex]

[tex]x = \frac{243}{5} [/tex]