Solve x-6x/2+12<8x+1/3-10x

$$\frac { x - 6 x } { 2 } + 12 < \frac { 8 x + 1 } { 3 } - 10 x$$

Solve for x

$$x<-\frac{70}{29}$$

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.

$$3\left(x-6x\right)+72<2\left(8x+1\right)-60x$$

Combine x and -6x to get -5x.

$$3\left(-5\right)x+72<2\left(8x+1\right)-60x$$

Multiply 3 and -5 to get -15.

$$-15x+72<2\left(8x+1\right)-60x$$

Use the distributive property to multiply 2 by 8x+1.

$$-15x+72<16x+2-60x$$

Combine 16x and -60x to get -44x.

$$-15x+72<-44x+2$$

Add 44x to both sides.

$$-15x+72+44x<2$$

Combine -15x and 44x to get 29x.

$$29x+72<2$$

Subtract 72 from both sides.

$$29x<2-72$$

Subtract 72 from 2 to get -70.

$$29x<-70$$

Divide both sides by 29. Since 29 is positive, the inequality direction remains the same.

$$x<-\frac{70}{29}$$