Solve the inequality x + 10 < 3x + 6.

Step-by-step solution

1. 1

   Collect the variable where its coefficient is larger. Subtracting $x$ from both sides sends the variable to the right with coefficient $3-1=2>0$:

   $10<2x+6$

2. 2

   Move the constant. Subtract $6$ from both sides:

   $4<2x$

3. 3

   Divide by $2$. A positive divisor leaves the direction alone:

   $2<x$

4. 4

   Present the answer with the variable first. Reading $2<x$ from the other end gives

   $x>2,\qquad\text{i.e. }(2,\infty)$

5. 5

   Check on both sides of $2$. At $x=10$: left $=20$, right $=36$, and $20<36$ $\checkmark$. At $x=0$: left $=10$, right $=6$, false $\checkmark$. At $x=2$ both sides equal $12$, so the strict inequality excludes the boundary.