Solve 5+x/6<31/6x-2

$$5 + \frac { x } { 6 } < 3 \frac { 1 } { 6 } x - 2$$

Solve for x

$$x>\frac{7}{3}$$

Solution Steps

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

$$30+x<\left(3\times 6+1\right)x-12$$

Multiply 3 and 6 to get 18.

$$30+x<\left(18+1\right)x-12$$

Add 18 and 1 to get 19.

$$30+x<19x-12$$

Subtract 19x from both sides.

$$30+x-19x<-12$$

Combine x and -19x to get -18x.

$$30-18x<-12$$

Subtract 30 from both sides.

$$-18x<-12-30$$

Subtract 30 from -12 to get -42.

$$-18x<-42$$

Divide both sides by -18. Since -18 is negative, the inequality direction is changed.

$$x>\frac{-42}{-18}$$

Reduce the fraction \frac{-42}{-18} to lowest terms by extracting and canceling out -6.

$$x>\frac{7}{3}$$