Solve the inequality 3x + 15 > 30 + 2x.

Step-by-step solution

1. 1

   Subtract $2x$ from both sides. The left coefficient is larger, so collecting there gives a positive result:

   $x+15>30$

2. 2

   Note that the coefficient is now exactly $1$. That means the final step is a subtraction, not a division, so there is no chance of a sign flip.

3. 3

   Subtract $15$ from both sides.

   $x>15$

4. 4

   Test either side of the boundary. At $x=20$: left $=75$, right $=70$, and $75>70$ $\checkmark$. At $x=0$: left $=15$, right $=30$, false $\checkmark$. At $x=15$ both sides equal $60$, so the strict inequality correctly leaves it out. Solution set: $(15,\infty)$.