Solve the inequality 3x - 5 > 2(x - 2).

Step-by-step solution

1. 1

   Distribute the $2$ over the bracket. Multiply both terms inside by $2$, taking care with the minus sign:

   $2(x-2)=2x-4\quad\Longrightarrow\quad 3x-5>2x-4$

2. 2

   Subtract $2x$ from both sides. The larger coefficient is on the left, so collecting there keeps things positive:

   $x-5>-4$

3. 3

   Add $5$ to both sides.

   $x>1$

   The coefficient of $x$ is already $1$, so there is no division step and therefore no opportunity for a sign flip.

4. 4

   Test the two regions and the boundary. At $x=5$: left $=10$, right $=6$, and $10>6$ $\checkmark$. At $x=0$: left $=-5$, right $=-4$, and $-5>-4$ is false $\checkmark$. At $x=1$ both sides equal $-2$, so the strict inequality rightly excludes it. Solution set: $(1,\infty)$.