Solve the inequality 2x - 7 < 3(x - 1).

Step-by-step solution

1. 1

   Expand the right-hand bracket.

   $3(x-1)=3x-3\quad\Longrightarrow\quad 2x-7<3x-3$

2. 2

   Subtract $2x$ from both sides. The bigger coefficient $3$ is on the right, so the variable naturally ends up there with a positive coefficient:

   $-7<x-3$

3. 3

   Add $3$ to both sides.

   $-4<x$

4. 4

   Rewrite with the variable on the left. Swapping the two sides of an inequality reverses the symbol — it does not change the meaning:

   $x>-4$

   This is bookkeeping, not the negative-division rule; both statements describe the same set $(-4,\infty)$.

5. 5

   Check three points. At $x=0$: left $=-7$, right $=-3$, and $-7<-3$ $\checkmark$. At $x=-10$: left $=-27$, right $=-33$, false $\checkmark$. At $x=-4$: both sides equal $-15$, correctly excluded by the strict $<$.