Question

Solve for x in the inequality 11|x + 1| < 44

Answer 1

`~~~~~~11|x+1| < 44\\\\\implies |x+1| < (44)/(11)\\\\\implies |x+1| < 4\\\\\implies x +1 > -4~~~ \text{and}~~~ x+1 < 4\\\\\implies x > -4-1~~~ \text{and}~~~~ x < 4-1\\\\\implies x > -5~~~~~~~~ \text{and}~~~~~ x < 3\\\\\text{Hence,}~~ -5 < x < 3`