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

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

Solve for x

$$x>-\frac{39}{22}$$

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.

$$3\left(2x-3\right)+72>24-16x$$

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

$$6x-9+72>24-16x$$

Add -9 and 72 to get 63.

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

Add 16x to both sides.

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

Combine 6x and 16x to get 22x.

$$22x+63>24$$

Subtract 63 from both sides.

$$22x>24-63$$

Subtract 63 from 24 to get -39.

$$22x>-39$$

Divide both sides by 22. Since 22 is positive, the inequality direction remains the same.

$$x>-\frac{39}{22}$$