Answer
$\textbf{(a)}\hspace{0.7cm} x=5$
$\textbf{(b)}\hspace{0.7cm} x=-\dfrac{5}{2}$
$\textbf{(c)}\hspace{0.7cm} x=512$
$\textbf{(d)}\hspace{0.7cm} x=15/2$
$\textbf{(e)}\hspace{0.7cm} x=-1\pm\sqrt{6}$
Work Step by Step
$\textbf{(a)}4x-3=2x+7\Rightarrow4x-2x=7+3\Rightarrow2x=10\Rightarrow x=5$
$\textbf{(b)}8x^3=-125\Rightarrow x^3=-\dfrac{125}{8}\Rightarrow x=\sqrt[3]{-\dfrac{125}{8}}\Rightarrow x=-\dfrac{5}{2}$
$\textbf{(c)}x^{2/3}-64=0\Rightarrow x^{2/3}=64\Rightarrow x=64^{3/2}\Rightarrow x=512$
$\textbf{(d)}\dfrac{x}{2x-5}=\dfrac{x+3}{2x-1}\Rightarrow x(2x-1)=(x+3)(2x-5)\Rightarrow 2x^2-x=2x^2+6x-5x-15\Rightarrow 2x^2-x=2x^2+x-15\Rightarrow 2x^2-x-2x^2-x=-15\Rightarrow -2x=-15\Rightarrow x=15/2$
$\textbf{(e)}3(x+1)^2-18=0\Rightarrow 3(x^2+2x+1)-18=0\Rightarrow 3x^2+6x-15=0$
Use the quadratic formula where $a=3$, $b=6$ and $c=15$
$x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-6\pm\sqrt{6^2-4(3)(-15)}}{2(3)}=\dfrac{-6\pm\sqrt{216}}{6}=-1\pm\sqrt{6}$
