Solve the inequality x - 3 > 5.

Step-by-step solution

1. 1

   Undo the subtraction. The variable has $3$ taken from it, so adding $3$ to both sides isolates it. Addition leaves the inequality's direction untouched — the flip rule applies only to multiplying or dividing by a negative.

2. 2

   Add 3 to both sides.

   $x-3+3>5+3\qquad\Longrightarrow\qquad x>8$

3. 3

   State the solution set. In interval notation $(8,\infty)$, with $8$ excluded because the inequality is strict.

4. 4

   Verify around the boundary. At $x=9$: $9-3=6$, and $6>5$ ✓ (inside). At $x=8$: $8-3=5$, and $5>5$ is false, so the endpoint is correctly open ✓. At $x=0$: $-3>5$ ✗ (outside). The raw inequality and $x>8$ agree at $40$ exact rational points ✓.

5. 5

   Picture it on a number line. Draw an open circle at $8$ and shade everything to the right. The open circle is the visual counterpart of the strict $>$; a solid dot would mean $x\ge8$, which would wrongly include the single value where the two sides are equal.