Given Information:

The compound inequality, \(\displaystyle-{4}\le-{\frac{{{2}}}{{{3}}}}{p}+{14}\)

Calculation:

The given compound inequality is \(\displaystyle-{4}\le-{\frac{{{2}}}{{{3}}}}{p}+{14}\). Subtract 14 from the inequality.

\(\displaystyle-{4}-{14}\le-{\frac{{{2}}}{{{3}}}}{p}+{14}-{14}\)

\(\displaystyle-{18}\le-{\frac{{{2}}}{{{3}}}}{p}\)

Divide the inequality by \(\displaystyle-{\frac{{{2}}}{{{3}}}}\) and change the sense of inequality,

\(\displaystyle{\frac{{-{18}}}{{{\left(-{\frac{{{2}}}{{{3}}}}\right)}}}}\geq{\frac{{-{\frac{{{2}}}{{{3}}}}}}{{{\left(-{\frac{{{2}}}{{{3}}}}\right)}}}}{p}\)

After division,

\(\displaystyle-{18}\times-{\frac{{{3}}}{{{2}}}}\geq-{\frac{{{2}}}{{{3}}}}\times-{\frac{{{3}}}{{{2}}}}{p}\)

\(\displaystyle{27}\geq{p}\)

The graph of the solution is:

Therefore, the solution set of compound inequality \(\displaystyle-{4}\le-{\frac{{{2}}}{{{3}}}}{p}+{14}\) is \(\displaystyle{\left\lbrace{p}{\mid}{p}\le{27}\right\rbrace}\) and interval notation is \(\displaystyle{\left(-\propto,{27}\right]}\).

The compound inequality, \(\displaystyle-{4}\le-{\frac{{{2}}}{{{3}}}}{p}+{14}\)

Calculation:

The given compound inequality is \(\displaystyle-{4}\le-{\frac{{{2}}}{{{3}}}}{p}+{14}\). Subtract 14 from the inequality.

\(\displaystyle-{4}-{14}\le-{\frac{{{2}}}{{{3}}}}{p}+{14}-{14}\)

\(\displaystyle-{18}\le-{\frac{{{2}}}{{{3}}}}{p}\)

Divide the inequality by \(\displaystyle-{\frac{{{2}}}{{{3}}}}\) and change the sense of inequality,

\(\displaystyle{\frac{{-{18}}}{{{\left(-{\frac{{{2}}}{{{3}}}}\right)}}}}\geq{\frac{{-{\frac{{{2}}}{{{3}}}}}}{{{\left(-{\frac{{{2}}}{{{3}}}}\right)}}}}{p}\)

After division,

\(\displaystyle-{18}\times-{\frac{{{3}}}{{{2}}}}\geq-{\frac{{{2}}}{{{3}}}}\times-{\frac{{{3}}}{{{2}}}}{p}\)

\(\displaystyle{27}\geq{p}\)

The graph of the solution is:

Therefore, the solution set of compound inequality \(\displaystyle-{4}\le-{\frac{{{2}}}{{{3}}}}{p}+{14}\) is \(\displaystyle{\left\lbrace{p}{\mid}{p}\le{27}\right\rbrace}\) and interval notation is \(\displaystyle{\left(-\propto,{27}\right]}\).