Answer
$-\dfrac{5}{8}$
Work Step by Step
Since $a-(-b)=a+b,$ the given expression, $
-\left| \dfrac{7}{8}-\left(-\dfrac{1}{2} \right) -\dfrac{3}{4} \right|
,$ is equivalent to
\begin{array}{l}\require{cancel}
-\left| \dfrac{7}{8}-\left(-\dfrac{1}{2} \right) -\dfrac{3}{4} \right|
\\\\=
-\left| \dfrac{7}{8}+\dfrac{1}{2} -\dfrac{3}{4} \right|
.\end{array}
The $LCD$ of the denominators, $\{8,2,4\}$ is $8$ since it is the least number that can be divided evenly (no remainder) by all the denominators. Using the $LCD$ to express the fractions as similar fractions (fractions with same denominator) results to
\begin{array}{l}\require{cancel}
-\left| \dfrac{7}{8}+\dfrac{1}{2} -\dfrac{3}{4} \right|
\\\\=
-\left| \dfrac{7}{8}+\dfrac{1}{2}\cdot\dfrac{4}{4} -\dfrac{3}{4}\cdot\dfrac{2}{2} \right|
\\\\=
-\left| \dfrac{7}{8}+\dfrac{4}{8} -\dfrac{6}{8} \right|
\\\\=
-\left| \dfrac{7+4-6}{8} \right|
\\\\=
-\left| \dfrac{5}{8} \right|
\\\\=
-\left( \dfrac{5}{8} \right)
\\\\=
-\dfrac{5}{8}
.\end{array}
