Solve the inequality 10x + 6 > 12x - 4.

Step-by-step solution

1. 1

   Choose which side collects the variable. The coefficients are $10$ on the left and $12$ on the right. Moving the smaller one to the right leaves $12x-10x=2x$, a positive coefficient — so no sign flip will be needed at the end.

2. 2

   Subtract $10x$ from both sides.

   $6>2x-4$

3. 3

   Add $4$ to both sides.

   $10>2x$

4. 4

   Divide by $2$ and read the result the usual way round. Since $2>0$ the direction is preserved:

   $5>x\quad\Longleftrightarrow\quad x<5$

   Both forms say the same thing; rewriting with the variable on the left just makes the answer easier to read.

5. 5

   Check both regions. At $x=0$: left $=6$, right $=-4$, and $6>-4$ $\checkmark$. At $x=10$: left $=106$, right $=116$, and $106>116$ is false $\checkmark$. At $x=5$ both sides equal $56$, so the boundary is excluded as the strict $>$ requires.