Answer
$\left[ \dfrac{7}{2}, -\infty\right)$
Work Step by Step
Using $a(b+c)=ab+ac$ (or the Distributive Property), and using the properties of inequality, the solution to the given expression, $
5(x-2)\ge3(x-1)
,$ is
\begin{array}{l}\require{cancel}
5x-10\ge3x-3
\\\\
5x-3x\ge-3+10
\\\\
2x\ge7
\\\\
x\ge\dfrac{7}{2}
.\end{array}
Hence, the solution is $
\left[ \dfrac{7}{2}, -\infty\right)
.$
