Question

What is m<2 + m<3? Explain.

Answer 1

`\large\boxed{m<1\to m\in(-\infty,\ 1)}`

Explanation:

`m<2+m<3\to m<2+m\ and\ 2+m<3\\\\m<2+m\qquad\text{subtract}\ m\ \text{from both sides}\\m-m<2+m-m\\0<2\qquad\bold{TRUE}\to m\in\mathbb{R}\ (all\ real\ numbers)\\\\2+m<3\qquad\text{subtract 2 from both sides}\\2-2+m<3-2\\m<1\\\\m\ \text{is any real number and}\ m<1.\\\\\text{Therefore}\ m<1\to m\in(-\infty,\ 1)`