Question

Solve each of the following system of equations in R. 

20. −5 < 2x − 3 < 5

Answer 1

\[- 5 < 2x - 3 < 5\]
\[ \Rightarrow - 5 + 3 < 2x < 5 + 3 \left( \text{ Adding 3 throughout } \right)\]
\[ \Rightarrow - 2 < 2x < 8\]
\[ \Rightarrow - 1 < x < 4 \left( \text{ Dividing throughout by } 2 \right)\]
\[ \Rightarrow x \in \left( - 1, 4 \right)\]
Hence, the interval(\[-\]1,4) is the solution of the given set of inequaltions.