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

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

Solve for x

$$x<\frac{3}{2}$$

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.

$$15-6x>2\left(3-2x\right)+6$$

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

$$15-6x>6-4x+6$$

Add 6 and 6 to get 12.

$$15-6x>12-4x$$

Add 4x to both sides.

$$15-6x+4x>12$$

Combine -6x and 4x to get -2x.

$$15-2x>12$$

Subtract 15 from both sides.

$$-2x>12-15$$

Subtract 15 from 12 to get -3.

$$-2x>-3$$

Divide both sides by -2. Since -2 is negative, the inequality direction is changed.

$$x<\frac{-3}{-2}$$

Fraction \frac{-3}{-2} can be simplified to \frac{3}{2} by removing the negative sign from both the numerator and the denominator.

$$x<\frac{3}{2}$$