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

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

Solve for x

$$x<2$$

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.

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

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

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

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

$$3x-6>4x-2-6$$

Subtract 6 from -2 to get -8.

$$3x-6>4x-8$$

Subtract 4x from both sides.

$$3x-6-4x>-8$$

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

$$-x-6>-8$$

Add 6 to both sides.

$$-x>-8+6$$

Add -8 and 6 to get -2.

$$-x>-2$$

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

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

Fraction \frac{-2}{-1} can be simplified to 2 by removing the negative sign from both the numerator and the denominator.

$$x<2$$