Solve 5-1-5x/3<10+x/6

$$5- \frac{ 1-5x }{ 3 } < \frac{ 10+x }{ 6 }$$

Solve for x

$$x<-2$$

Solution Steps

Multiply both sides of the equation by 6, the least common multiple of 3,6. Since 6 is positive, the inequality direction remains the same.

$$30-2\left(1-5x\right)<10+x$$

Use the distributive property to multiply -2 by 1-5x.

$$30-2+10x<10+x$$

Subtract 2 from 30 to get 28.

$$28+10x<10+x$$

Subtract x from both sides.

$$28+10x-x<10$$

Combine 10x and -x to get 9x.

$$28+9x<10$$

Subtract 28 from both sides.

$$9x<10-28$$

Subtract 28 from 10 to get -18.

$$9x<-18$$

Divide both sides by 9. Since 9 is positive, the inequality direction remains the same.

$$x<\frac{-18}{9}$$

Divide -18 by 9 to get -2.

$$x<-2$$