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

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

Solve for x

$$x<\frac{9}{31}$$

Solution Steps

Multiply both sides of the equation by 10, the least common multiple of 5,2. Since 10 is positive, the inequality direction remains the same.

$$2\left(2-3x\right)>30x-5\left(1+x\right)$$

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

$$4-6x>30x-5\left(1+x\right)$$

Use the distributive property to multiply -5 by 1+x.

$$4-6x>30x-5-5x$$

Combine 30x and -5x to get 25x.

$$4-6x>25x-5$$

Subtract 25x from both sides.

$$4-6x-25x>-5$$

Combine -6x and -25x to get -31x.

$$4-31x>-5$$

Subtract 4 from both sides.

$$-31x>-5-4$$

Subtract 4 from -5 to get -9.

$$-31x>-9$$

Divide both sides by -31. Since -31 is negative, the inequality direction is changed.

$$x<\frac{-9}{-31}$$

Fraction \frac{-9}{-31} can be simplified to \frac{9}{31} by removing the negative sign from both the numerator and the denominator.

$$x<\frac{9}{31}$$