Question

Solve the following inequation, write the solution set and represent it on the number line.

`-3(x - 7) >= 15 - 7x > (x+1)/3`, x ∉ R

Answer 1

`-3(x - 7) >= 15 - 7x > (x+1)/3`

`=> -3(x - 7)>= 15 - 7x` and `15 - 7x >(x+1)/3`

`=> -3x + 21 >= 15 - 7x` and 45 - 21x > x + 1

`=>4x >= -6` and 44 > 22x

`=> x >= (-3)/2` and 2 > x

`=> x >=  -1.5 and 2 > x`

The solution set is `{x : x ∈ R, -1.5 <= x < 2}`