Question

Solve the following system of equation in R. 

 x + 5 > 2(x + 1), 2 − x < 3 (x + 2)

Answer 1

x + 5 > 2(x + 1) and 2 − x < 3(x + 2)

x + 5 > 2x + 2     2 − x < 3x + 6

5 − 2 > 2x − x      2 − 6 < 3x + x

3 > x         4x > −4

x < 3    and    x > −1

Hence, x ∈ (−1, 3) R