Solve 3/4x-5/2x>2(x-3)/8

$$\frac{ 3 }{ 4 } x- \frac{ 5 }{ 2 } x > \frac{ 2(x-3) }{ 8 }$$

Solve for x

$$x<\frac{3}{8}$$

Solution Steps

Multiply both sides of the equation by 8, the least common multiple of 4,2,8. Since 8 is positive, the inequality direction remains the same.

$$6x-20x>2\left(x-3\right)$$

Combine 6x and -20x to get -14x.

$$-14x>2\left(x-3\right)$$

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

$$-14x>2x-6$$

Subtract 2x from both sides.

$$-14x-2x>-6$$

Combine -14x and -2x to get -16x.

$$-16x>-6$$

Divide both sides by -16. Since -16 is negative, the inequality direction is changed.

$$x<\frac{-6}{-16}$$

Reduce the fraction \frac{-6}{-16} to lowest terms by extracting and canceling out -2.

$$x<\frac{3}{8}$$