Solve the inequality 4 - 2m - m + 3 > 0.

Step-by-step solution

1. 1

   Sort the four terms into two groups. The constants are $4$ and $+3$; the variable terms are $-2m$ and $-m$. Grouping like with like:

   $4+3=7,\qquad -2m-m=-3m$

2. 2

   Rewrite the simplified inequality.

   $7-3m>0$

3. 3

   Add $3m$ to both sides instead of dividing by a negative. This keeps the variable coefficient positive and removes any need for a sign flip:

   $7>3m$

4. 4

   Divide by $3$ and rewrite with $m$ first.

   $\frac{7}{3}>m\quad\Longleftrightarrow\quad m<\frac{7}{3}$

5. 5

   Confirm with test values. At $m=0$: $4-0-0+3=7>0$ $\checkmark$. At $m=3$: $4-6-3+3=-2\not>0$ $\checkmark$. At $m=\tfrac73$: $7-3\cdot\tfrac73=0$, which is not $>0$, so the boundary is correctly excluded.