Solve x/6+1>x+2/3

$$\frac { x } { 6 } + 1 > \frac { x + 2 } { 3 }$$

Solve for x

$$x<2$$

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.

$$x+6>2\left(x+2\right)$$

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

$$x+6>2x+4$$

Subtract 2x from both sides.

$$x+6-2x>4$$

Combine x and -2x to get -x.

$$-x+6>4$$

Subtract 6 from both sides.

$$-x>4-6$$

Subtract 6 from 4 to get -2.

$$-x>-2$$

Divide both sides by -1. Since -1 is negative, the inequality direction is changed.

$$x<\frac{-2}{-1}$$

Fraction \frac{-2}{-1} can be simplified to 2 by removing the negative sign from both the numerator and the denominator.

$$x<2$$