Question

Solve the following system of equations in R.

x+5>2(x+1),2-x<3(x+2)

Answer 1

Consider the first inequation,

x+5>2(x+1)

x>2x+2-5

x>2x-3

x-2>-3

-x>-3

x<3

Consider the second inequation,

2-x<3(x+2)

2-x<3x+6

-x-3x<6-2

-4x<4

x>-1

From (i) and (ii),(-1,3) is the solution set of the simultaneous equations.