Solve x-2/6+2x-5/8>12x-5/24

$$\frac{ x-2 }{ 6 } + \frac{ 2x-5 }{ 8 } > \frac{ 12x-5 }{ 24 }$$

Solve for x

$$x<-9$$

Solution Steps

Multiply both sides of the equation by 24, the least common multiple of 6,8,24. Since 24 is positive, the inequality direction remains the same.

$$4\left(x-2\right)+3\left(2x-5\right)>12x-5$$

Use the distributive property to multiply 4 by x-2.

$$4x-8+3\left(2x-5\right)>12x-5$$

Use the distributive property to multiply 3 by 2x-5.

$$4x-8+6x-15>12x-5$$

Combine 4x and 6x to get 10x.

$$10x-8-15>12x-5$$

Subtract 15 from -8 to get -23.

$$10x-23>12x-5$$

Subtract 12x from both sides.

$$10x-23-12x>-5$$

Combine 10x and -12x to get -2x.

$$-2x-23>-5$$

Add 23 to both sides.

$$-2x>-5+23$$

Add -5 and 23 to get 18.

$$-2x>18$$

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

$$x<\frac{18}{-2}$$

Divide 18 by -2 to get -9.

$$x<-9$$