x on Both Sides

An inequality can have $x$ on both sides. To solve $3x+2 > x+8$, first collect the x-terms on one side. Subtract $x$ from both sides. An x-term is subtracted like any number, and subtracting never flips the sign. Then move the numbers to the other side, and divide.

$$2x+2 > 8$$

$$2x > 6$$

$$x > 3$$

Check with a number above 3, such as 4. The left side is $3\cdot 4+2 = 14$ and the right side is $4+8 = 12$. Since 14 is greater than 12, the answer works.

The steps are the same as for an equation with $x$ on both sides. Move the x-terms to one side, move the numbers to the other side, then divide. Each of these steps is an addition, a subtraction or a division by a positive number, so the sign keeps its direction.