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

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

Solve for x

$$x<\frac{27}{19}$$

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.

$$3\left(x+3\right)-12x>2\left(5x-3\right)-12$$

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

$$3x+9-12x>2\left(5x-3\right)-12$$

Combine 3x and -12x to get -9x.

$$-9x+9>2\left(5x-3\right)-12$$

Use the distributive property to multiply 2 by 5x-3.

$$-9x+9>10x-6-12$$

Subtract 12 from -6 to get -18.

$$-9x+9>10x-18$$

Subtract 10x from both sides.

$$-9x+9-10x>-18$$

Combine -9x and -10x to get -19x.

$$-19x+9>-18$$

Subtract 9 from both sides.

$$-19x>-18-9$$

Subtract 9 from -18 to get -27.

$$-19x>-27$$

Divide both sides by -19. Since -19 is negative, the inequality direction is changed.

$$x<\frac{-27}{-19}$$

Fraction \frac{-27}{-19} can be simplified to \frac{27}{19} by removing the negative sign from both the numerator and the denominator.

$$x<\frac{27}{19}$$