Step 1: To Find

We have to solve the linear equation in one variable and rational equations.

Step 2: Explanation

If we have a linear equation \(\displaystyle\frac{{5}}{{2}}{x}+\frac{{2}}{{3}}=−\frac{{7}}{{12}}\) then the solution

\(\displaystyle\frac{{5}}{{2}}{x}+\frac{{2}}{{3}}=-\frac{{7}}{{12}}\)

\(\displaystyle\frac{{{15}{x}+{4}}}{{6}}=-\frac{{7}}{{12}}\)

\(\displaystyle{\left({15}{x}+{4}\right)}=-\frac{{{7}\times{6}}}{{12}}\)

\(\displaystyle{\left({15}{x}+{4}\right)}=-\frac{{7}}{{2}}\)

2(15x+4)=-7

30x+8=-7

30x=-7-8

30x=-15

\(\displaystyle{x}=-\frac{{15}}{{30}}\)

\(\displaystyle{x}=-\frac{{1}}{{2}}\)

We have to solve the linear equation in one variable and rational equations.

Step 2: Explanation

If we have a linear equation \(\displaystyle\frac{{5}}{{2}}{x}+\frac{{2}}{{3}}=−\frac{{7}}{{12}}\) then the solution

\(\displaystyle\frac{{5}}{{2}}{x}+\frac{{2}}{{3}}=-\frac{{7}}{{12}}\)

\(\displaystyle\frac{{{15}{x}+{4}}}{{6}}=-\frac{{7}}{{12}}\)

\(\displaystyle{\left({15}{x}+{4}\right)}=-\frac{{{7}\times{6}}}{{12}}\)

\(\displaystyle{\left({15}{x}+{4}\right)}=-\frac{{7}}{{2}}\)

2(15x+4)=-7

30x+8=-7

30x=-7-8

30x=-15

\(\displaystyle{x}=-\frac{{15}}{{30}}\)

\(\displaystyle{x}=-\frac{{1}}{{2}}\)