Solve 2(3x-1)-4>3(4x-6)-2

$$2 ( 3 x - 1 ) - 4 > 3 ( 4 x - 6 ) - 2$$

Solve for x

$$x<\frac{7}{3}$$

Solution Steps

Use the distributive property to multiply 2 by 3x-1.

$$6x-2-4>3\left(4x-6\right)-2$$

Subtract 4 from -2 to get -6.

$$6x-6>3\left(4x-6\right)-2$$

Use the distributive property to multiply 3 by 4x-6.

$$6x-6>12x-18-2$$

Subtract 2 from -18 to get -20.

$$6x-6>12x-20$$

Subtract 12x from both sides.

$$6x-6-12x>-20$$

Combine 6x and -12x to get -6x.

$$-6x-6>-20$$

Add 6 to both sides.

$$-6x>-20+6$$

Add -20 and 6 to get -14.

$$-6x>-14$$

Divide both sides by -6. Since -6 is negative, the inequality direction is changed.

$$x<\frac{-14}{-6}$$

Reduce the fraction \frac{-14}{-6} to lowest terms by extracting and canceling out -2.

$$x<\frac{7}{3}$$