Answer
$x\approx-0.17$
Work Step by Step
By cross-multiplication, the solution to the given equation, $
\dfrac{1.4}{x-2.6}=\dfrac{-3.5}{x+7.1}
,$ is equivalent to
\begin{array}{l}\require{cancel}
1.4(x+7.1)=-3.5(x-2.6)
\\\\
1.4x+9.94=-3.5x+9.1
\\\\
1.4x+3.5x=9.1-9.94
\\\\
4.9x=-0.84
\\\\
x=-\dfrac{0.84}{4.9}
\\\\
x\approx-0.17
.\end{array}
