Answer
$\text{the interval }\left[ -\dfrac{15}{4},-\dfrac{3}{4} \right)$
Work Step by Step
Using the properties of inequalities, then,
\begin{array}{l}
-0.7\le 0.4x+0.8\lt0.5\\
-7\le 4x+8\lt5
\text{...multiply all sides by 10}\\
-15\le 4x\lt-3\\\\
-\dfrac{15}{4}\le x\lt-\dfrac{3}{4}
.\end{array}
Hence, in interval notation form, the solution is $
\text{the interval }\left[ -\dfrac{15}{4},-\dfrac{3}{4} \right)
$.
