Solve 1-x-1/6<2x+1/3

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

Solve for x

$$x>1$$

Solution Steps

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

$$6-\left(x-1\right)<2\left(2x+1\right)$$

To find the opposite of x-1, find the opposite of each term.

$$6-x-\left(-1\right)<2\left(2x+1\right)$$

The opposite of -1 is 1.

$$6-x+1<2\left(2x+1\right)$$

Add 6 and 1 to get 7.

$$7-x<2\left(2x+1\right)$$

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

$$7-x<4x+2$$

Subtract 4x from both sides.

$$7-x-4x<2$$

Combine -x and -4x to get -5x.

$$7-5x<2$$

Subtract 7 from both sides.

$$-5x<2-7$$

Subtract 7 from 2 to get -5.

$$-5x<-5$$

Divide both sides by -5. Since -5 is negative, the inequality direction is changed.

$$x>\frac{-5}{-5}$$

Divide -5 by -5 to get 1.

$$x>1$$