Solve 1-2x/3>4-3x/6

$$\frac { 1 - 2 x } { 3 } > \frac { 4 - 3 x } { 6 }$$

Solve for x

$$x<-2$$

Solution Steps

Multiply both sides of the equation by 6, the least common multiple of 3,6. Since 6 is positive, the inequality direction remains the same.

$$2\left(1-2x\right)>4-3x$$

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

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

Add 3x to both sides.

$$2-4x+3x>4$$

Combine -4x and 3x to get -x.

$$2-x>4$$

Subtract 2 from both sides.

$$-x>4-2$$

Subtract 2 from 4 to get 2.

$$-x>2$$

Divide both sides by -1. Since -1 is negative, the inequality direction is changed.

$$x<-2$$