Solve the Inequality for x 3(2x-1)>4x-2

$3 (2 x - 1) > 4 x - 2$

Simplify $3 (2 x - 1)$ .

Rewrite.

$0 + 0 + 3 (2 x - 1) > 4 x - 2$

Simplify by adding zeros.

$3 (2 x - 1) > 4 x - 2$

Apply the distributive property.

$3 (2 x) + 3 \cdot - 1 > 4 x - 2$

Multiply.

Multiply $2$ by $3$ .

$6 x + 3 \cdot - 1 > 4 x - 2$

Multiply $3$ by $- 1$ .

$6 x - 3 > 4 x - 2$

Move all terms containing $x$ to the left side of the inequality.

Subtract $4 x$ from both sides of the inequality.

$6 x - 3 - 4 x > - 2$

Subtract $4 x$ from $6 x$ .

$2 x - 3 > - 2$

Move all terms not containing $x$ to the right side of the inequality.

Add $3$ to both sides of the inequality.

$2 x > - 2 + 3$

Add $- 2$ and $3$ .

$2 x > 1$

Divide each term in $2 x > 1$ by $2$ and simplify.

Divide each term in $2 x > 1$ by $2$ .

$\frac{2 x}{2} > \frac{1}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} > \frac{1}{2}$

Divide $x$ by $1$ .

$x > \frac{1}{2}$

The result can be shown in multiple forms.

Inequality Form:

$x > \frac{1}{2}$

Interval Notation:

$(\frac{1}{2}, \infty)$