Solve x-3/2-1>x-5/3

$$\frac { x - 3 } { 2 } - 1 > \frac { x - 5 } { 3 }$$

Solve for x

$$x>5$$

Solution Steps

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

$$3\left(x-3\right)-6>2\left(x-5\right)$$

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

$$3x-9-6>2\left(x-5\right)$$

Subtract 6 from -9 to get -15.

$$3x-15>2\left(x-5\right)$$

Use the distributive property to multiply 2 by x-5.

$$3x-15>2x-10$$

Subtract 2x from both sides.

$$3x-15-2x>-10$$

Combine 3x and -2x to get x.

$$x-15>-10$$

Add 15 to both sides.

$$x>-10+15$$

Add -10 and 15 to get 5.

$$x>5$$