Answer
$\left( -\infty,\dfrac{76}{11} \right)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
-\dfrac{1}{4}(p+6)+\dfrac{3}{2}(2p-5)\lt10
,$ 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 and the properties of inequality, the inequality above is equivalent to
\begin{array}{l}\require{cancel}
4\left(-\dfrac{1}{4}(p+6)+\dfrac{3}{2}(2p-5)\right)\lt4(10)
\\\\
-1(p+6)+6(2p-5)\lt40
\\\\
-p-6+12p-30\lt40
\\\\
-p+12p\lt40+6+30
\\\\
11p\lt76
\\\\
p\lt\dfrac{76}{11}
.\end{array}
The red graph is the graph of the solution set.
In interval notation, the solution set is $
\left( -\infty,\dfrac{76}{11} \right)
.$
