Solve the inequality 7x + 11 > 3(x + 1).

Step-by-step solution

1. 1

   Expand the bracket on the right. Multiply the $3$ by both terms inside:

   $3(x+1)=3x+3\quad\Longrightarrow\quad 7x+11>3x+3$

   Distributing before rearranging keeps the bookkeeping simple; trying to divide by $3$ first would put a fraction on the left.

2. 2

   Collect the variable terms on the side with the larger coefficient. Subtract $3x$ from both sides so the $x$ coefficient stays positive:

   $4x+11>3$

3. 3

   Move the constant across. Subtract $11$:

   $4x>-8$

4. 4

   Divide by $4$. Since $4>0$, the direction of the inequality is unchanged:

   $x>-2$

5. 5

   Verify with test values. At $x=0$: left $=11$, right $=3$, and $11>3$ $\checkmark$. At $x=-3$: left $=-10$, right $=-6$, and $-10>-6$ is false $\checkmark$. At the boundary $x=-2$ both sides equal $-3$, so the endpoint is correctly excluded by the strict inequality.