Question

Solve the given inequality for real x: x + `x/2` + `x/3` < 11

Answer 1

`x  + x/2` + `x/3` <11`

= `x(1 + 1/2 + 1/3) < 11`

= `(6x + 3x + 2x)/6 < 11`

 = `(11x)/6 < 11`

= `(11x)/(6 xx 11) < 11/11`

= `x/6 < 1`

= x < 6

Thus, all real numbers x, which are less than 6, are the solutions of the given inequality.

Hence, the solution set of the given inequality is (–∞, 6).