Solve the inequality x - 3(x - 2) >= 4.

Step-by-step solution

1. 1

   Distribute $-3$, not $3$. The bracket carries a minus sign in front of the $3$, so both inner terms are multiplied by $-3$:

   $-3(x-2)=-3x+6$

   The sign of the second term is the trap: $-3\times(-2)=+6$.

2. 2

   Rewrite and combine like terms.

   $x-3x+6\ge 4\quad\Longrightarrow\quad -2x+6\ge 4$

3. 3

   Isolate the variable term. Subtract $6$ from both sides:

   $-2x\ge -2$

4. 4

   Divide by $-2$ and reverse the inequality.

   $x\le 1$

5. 5

   Check three values. At $x=1$: $1-3(-1)=1+3=4\ge 4$ $\checkmark$ (endpoint included). At $x=-2$: $-2-3(-4)=-2+12=10\ge 4$ $\checkmark$. At $x=5$: $5-3(3)=-4\not\ge 4$ $\checkmark$. Solution set: $(-\infty,1]$.