Solve the inequality x + 2 < 6.

Step-by-step solution

1. 1

   Pick the inverse operation. The variable has $2$ added to it, so subtracting $2$ isolates it. Subtracting the same number from both sides never changes an inequality's direction.

2. 2

   Subtract 2 from both sides.

   $x+2-2<6-2\qquad\Longrightarrow\qquad x<4$

3. 3

   State the solution set. In interval notation $(-\infty,4)$, with $4$ excluded because the relation is strict.

4. 4

   Verify around the boundary. At $x=3$: $3+2=5$, and $5<6$ ✓ (inside). At $x=4$: $4+2=6$, and $6<6$ is false — endpoint correctly open ✓. At $x=5$: $7<6$ ✗ (outside). The raw inequality and $x<4$ agree at $50$ exact rational points ✓.

5. 5

   Note that the solution is unbounded below. Every number less than $4$ works, including large negative ones: at $x=-100$, $-98<6$ ✓. There is no smallest solution, which is why the interval is written with $-\infty$ and always takes a round bracket — infinity is never an attainable endpoint.