Solve 2x-1/3<1-2x+1/2

$$\frac{ 2x-1 }{ 3 } < 1- \frac{ 2x+1 }{ 2 }$$

Solve for x

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

Solution Steps

Multiply both sides of the equation by 6, the least common multiple of 3,2. Since 6 is positive, the inequality direction remains the same.

$$2\left(2x-1\right)<6-3\left(2x+1\right)$$

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

$$4x-2<6-3\left(2x+1\right)$$

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

$$4x-2<6-6x-3$$

Subtract 3 from 6 to get 3.

$$4x-2<3-6x$$

Add 6x to both sides.

$$4x-2+6x<3$$

Combine 4x and 6x to get 10x.

$$10x-2<3$$

Add 2 to both sides.

$$10x<3+2$$

Add 3 and 2 to get 5.

$$10x<5$$

Divide both sides by 10. Since 10 is positive, the inequality direction remains the same.

$$x<\frac{5}{10}$$

Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

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