Question

6. Решите уравнение: 0, 5|4x - 1| — 6 = −5, 5 ​

Answer 1

$0,5|4x-1|-6=-5,5\Leftrightarrow \frac{1}{2}|4x-1|-6=-\frac{11}{2}\Leftrightarrow \frac{1}{2}|4x-1|=\frac{1}{2}\\|4x-1|=1\Leftrightarrow (4x-1)^2=1^1\Leftrightarrow (4x-1-1)(4x-1+1)=0\Leftrightarrow 4x(4x-2)=0\\x(2x-1)=0\Rightarrow \left[ \begin{gathered} x=0\\ 2x-1=0 \end{gathered} \right.\Rightarrow x=\left \{ 0,\frac{1}{2} \right \}$