Answer
from $67$ to $94$
Work Step by Step
Let $x$ be the final exam score.
The conditions of the problem translate to
\begin{array}{l}\require{cancel}
70\le\dfrac{68+65+75+78+2x}{6}\le79
.\end{array}
Using the properties of inequality, then
\begin{array}{l}\require{cancel}
70\le\dfrac{286+2x}{6}\le79
\\\\
6\cdot70\le6\cdot\dfrac{286+2x}{6}\le6\cdot79
\\\\
420\le286+2x\le474
\\\\
420-286\le286-286+2x\le474-286
\\\\
134\le2x\le188
\\\\
\dfrac{134}{2}\le\dfrac{2x}{2}\le\dfrac{188}{2}
\\\\
67\le x\le 94
.\end{array}
Hence, the final exam score can be any of the scores $\text{
from $67$ to $94$
.}$
