Solve 5x-3/3-3-x/6>2-x/12

$$\frac { 5 x - 3 } { 3 } - \frac { 3 - x } { 6 } > \frac { 2 - x } { 12 }$$

Solve for x

$$x>\frac{20}{23}$$

Solution Steps

Multiply both sides of the equation by 12, the least common multiple of 3,6,12. Since 12 is positive, the inequality direction remains the same.

$$4\left(5x-3\right)-2\left(3-x\right)>2-x$$

Use the distributive property to multiply 4 by 5x-3.

$$20x-12-2\left(3-x\right)>2-x$$

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

$$20x-12-6+2x>2-x$$

Subtract 6 from -12 to get -18.

$$20x-18+2x>2-x$$

Combine 20x and 2x to get 22x.

$$22x-18>2-x$$

Add x to both sides.

$$22x-18+x>2$$

Combine 22x and x to get 23x.

$$23x-18>2$$

Add 18 to both sides.

$$23x>2+18$$

Add 2 and 18 to get 20.

$$23x>20$$

Divide both sides by 23. Since 23 is positive, the inequality direction remains the same.

$$x>\frac{20}{23}$$