Answer
$\left( -\infty,\lt\dfrac{71}{150} \right)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
\dfrac{7}{5}(10x-1)\lt\dfrac{2}{3}(6x+5)
,$ use the Distributive Property and the properties of inequality.
For the interval notation, use a parenthesis for the symbols $\lt$ or $\gt.$ Use a bracket for the symbols $\le$ or $\ge.$
For graphing inequalities, use a hollowed dot for the symbols $\lt$ or $\gt.$ Use a solid dot for the symbols $\le$ or $\ge.$
$\bf{\text{Solution Details:}}$
Using the Distributive Property, the inequality above is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{7}{5}(10x)+\dfrac{7}{5}(-1)\lt\dfrac{2}{3}(6x)+\dfrac{2}{3}(5)
\\\\
14x-\dfrac{7}{5}\lt4x+\dfrac{10}{3}
.\end{array}
Using the properties of inequality, the inequality above is equivalent to
\begin{array}{l}\require{cancel}
15\left( 14x-\dfrac{7}{5} \right) \lt15\left( 4x+\dfrac{10}{3} \right)
\\\\
210x-21\lt60x+50
\\\\
210x-60x\lt50+21
\\\\
150x\lt71
\\\\
x\lt\dfrac{71}{150}
.\end{array}
The red graph is the graph of the solution set.
In interval notation, the solution set is $
\left( -\infty,\lt\dfrac{71}{150} \right)
.$
