Answer
$\left\{ x|x\ge\dfrac{64}{17} \right\}
\text{ or }
\left[ \dfrac{64}{17},\infty \right)
$
Work Step by Step
Using the properties of inequality, the given inequality, $
2(3+5x)\ge7(10-x)
,$ is equivalent to
\begin{array}{l}\require{cancel}
6+10x\ge70-7x
\\\\
10x+7x\ge70-6
\\\\
17x\ge64
\\\\
x\ge\dfrac{64}{17}
.\end{array}
Hence, the solution is $
\left\{ x|x\ge\dfrac{64}{17} \right\}
\text{ or }
\left[ \dfrac{64}{17},\infty \right)
.$
