[tex]-\dfrac{2}{3}\left(2x-\dfrac{1}{2}\right)\leq\dfrac{1}{5}x-1\ \ \ \ \text{use distributive property}\\\\-\dfrac{4}{3}x+\dfrac{1}{3}\leq\dfrac{1}{5}x-1\ \ \ \ \ |\cdot15\\\\-5(4x)+5\leq3x-15\\\\-20x+5\leq3x-15\ \ \ \ \ |-5\\\\-20x\leq3x-20\ \ \ \ |-3x\\\\-23x\leq-20\ \ \ \text{change the signs} \\\\23x\geq20\ \ \ \ \ \ |:23\\\\\boxed{x\geq\dfrac{20}{23}}\to x\in\left[\dfrac{20}{23},\ \infty\right)[/tex]
