Solve the inequality 2x - (x - 1) <= 1.

Step-by-step solution

1. 1

   Treat the minus sign as multiplication by $-1$. A bracket preceded by a minus flips the sign of every term inside, not just the first:

   $-(x-1)=-x+1$

   Writing $-x-1$ instead is the classic error here and would change the final answer.

2. 2

   Rewrite the inequality without brackets.

   $2x-x+1\le 1$

3. 3

   Combine the like terms. $2x-x=x$, so

   $x+1\le 1$

4. 4

   Subtract $1$ from both sides. No division is needed and no sign flips:

   $x\le 0,\qquad\text{i.e. }(-\infty,0]$

5. 5

   Check the boundary and a point on each side. At $x=0$: $0-(0-1)=1\le 1$ $\checkmark$, so $0$ is included. At $x=-5$: $-10-(-6)=-4\le 1$ $\checkmark$. At $x=3$: $6-2=4\not\le 1$ $\checkmark$.