Solve the equation: 3(2x+1) − 2x = x+1

Distribute the 3 into the parenthesis $(2x+1)$:

$$3(2x+1) - 2x = (x+1)$$ $$6x + 3 - 2x = x+1$$

Combine the $x$ terms on the left side:

$$(6x - 2x) + 3 = x+1$$ $$4x + 3 = x+1$$

Subtract $x$ from both sides:

$$4x - x + 3 = 1$$ $$3x + 3 = 1$$

Subtract 3 from both sides:

$$3x = 1 - 3$$ $$3x = -2$$

Divide both sides by 3:

$$x = \frac{-2}{3}$$

The solution is $x = -\frac{2}{3}$.