Question

Решите уравнение:
3/4|6х-3|+9,2=11
Даю 30 баллов!

Answer 1

$\displaystyle \tt \frac{3}{4}\cdot|6x-3|+9,2=11\\\\ \displaystyle \tt \frac{3}{4}\cdot|6x-3|+\frac{46}{5}=11\:\:\:\:\:\bigg|\cdot20\\\\ \displaystyle \tt 15\cdot|6x-3|+184=220\\\\ \displaystyle \tt 15\cdot|6x-3|=220-184\\\\ \displaystyle \tt 15\cdot|6x-3|=36\:\:\:\:\:\bigg|\div15\\\\ \displaystyle \tt |6x-3|=\frac{12}{5}$

$\displaystyle \tt 6x-3=\frac{12}{5} \: \: \: \: \: \bigg| \cdot5\\\\ \displaystyle \tt 5(6x-3)=12\\\\ \displaystyle \tt 30x-15=12\\\\ \displaystyle \tt 30x=12+15\\\\ \displaystyle \tt 30x=27\\\\ \displaystyle \tt x=27\div30\\\\ \displaystyle \tt \boxed{\bold{x_1=0,9}}$

$\displaystyle \tt 6x-3=-\frac{12}{5}\:\:\:\:\:\bigg|\div5\\\\ \displaystyle \tt 5(6x-3)=-12\\\\ \displaystyle \tt 30x-15=-12\\\\\displaystyle \tt 30x=-12+15\\\\ \displaystyle \tt 30x=3\\\\ \displaystyle \tt x=3\div30\\\\ \displaystyle \tt \boxed{\bold{x_2=0,1}}$