Solve 2x-3/4+6>2+4x/3

$$\frac { 2 x - 3 } { 4 } + 6 > 2 + \frac { 4 x } { 3 }$$

Solve for x

$$x<\frac{39}{10}$$

Solution Steps

Multiply both sides of the equation by 12, the least common multiple of 4,3. Since 12 is positive, the inequality direction remains the same.

$$3\left(2x-3\right)+72>24+4\times 4x$$

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

$$6x-9+72>24+4\times 4x$$

Add -9 and 72 to get 63.

$$6x+63>24+4\times 4x$$

Multiply 4 and 4 to get 16.

$$6x+63>24+16x$$

Subtract 16x from both sides.

$$6x+63-16x>24$$

Combine 6x and -16x to get -10x.

$$-10x+63>24$$

Subtract 63 from both sides.

$$-10x>24-63$$

Subtract 63 from 24 to get -39.

$$-10x>-39$$

Divide both sides by -10. Since -10 is negative, the inequality direction is changed.

$$x<\frac{-39}{-10}$$

Fraction \frac{-39}{-10} can be simplified to \frac{39}{10} by removing the negative sign from both the numerator and the denominator.

$$x<\frac{39}{10}$$