Solve the inequality 3x - 2x - 1 >= 0.

Step-by-step solution

1. 1

   Simplify before solving. The left-hand side contains two like terms in $x$; adding their coefficients first turns a three-term expression into a two-term one:

   $3x-2x=(3-2)x=x$

2. 2

   Rewrite the inequality.

   $x-1\ge 0$

3. 3

   Add $1$ to both sides. Adding a constant never changes the direction of an inequality:

   $x\ge 1$

4. 4

   Check the boundary and one point each side. At $x=1$: $3-2-1=0\ge 0$ $\checkmark$, so the endpoint belongs. At $x=4$: $12-8-1=3\ge 0$ $\checkmark$. At $x=0$: $0-0-1=-1\not\ge 0$ $\checkmark$. The solution set is $[1,\infty)$.