Solve the inequality x - 4 > 11.

Step-by-step solution

1. 1

   Choose the inverse operation. The variable has $4$ subtracted from it, so adding $4$ isolates it. Adding the same number to both sides preserves the inequality's direction — only multiplying or dividing by a negative would flip it, and that never happens here.

2. 2

   Add 4 to both sides.

   $x-4+4>11+4\qquad\Longrightarrow\qquad x>15$

3. 3

   State the solution set. In interval notation $(15,\infty)$, with $15$ excluded because the relation is strict.

4. 4

   Verify around the boundary. At $x=16$: $16-4=12$, and $12>11$ ✓ (inside). At $x=15$: $15-4=11$, and $11>11$ is false, so the endpoint is correctly open ✓. At $x=12$: $8>11$ ✗ (outside). The raw inequality and $x>15$ agree at $50$ exact rational points ✓.

5. 5

   Note the shortcut. For $x-c>d$ the answer is always $x>c+d$; here $4+11=15$ ✓. Recognising the pattern turns the problem into a single addition, and it doubles as a check on the algebra.