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

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

Solve for x

$$x<\frac{15}{8}$$

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.

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

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

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

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

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

Add 6 and 3 to get 9.

$$2x-6<9-6x$$

Add 6x to both sides.

$$2x-6+6x<9$$

Combine 2x and 6x to get 8x.

$$8x-6<9$$

Add 6 to both sides.

$$8x<9+6$$

Add 9 and 6 to get 15.

$$8x<15$$

Divide both sides by 8. Since 8 is positive, the inequality direction remains the same.

$$x<\frac{15}{8}$$