Solve x-x/2+x+1/3<1+x+5/6

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

Solve for x

$$x<\frac{9}{4}$$

Solution Steps

Multiply both sides of the equation by 6, the least common multiple of 2,3,6. Since 6 is positive, the inequality direction remains the same.

$$6x-3x+2\left(x+1\right)<6+x+5$$

Combine 6x and -3x to get 3x.

$$3x+2\left(x+1\right)<6+x+5$$

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

$$3x+2x+2<6+x+5$$

Combine 3x and 2x to get 5x.

$$5x+2<6+x+5$$

Add 6 and 5 to get 11.

$$5x+2<11+x$$

Subtract x from both sides.

$$5x+2-x<11$$

Combine 5x and -x to get 4x.

$$4x+2<11$$

Subtract 2 from both sides.

$$4x<11-2$$

Subtract 2 from 11 to get 9.

$$4x<9$$

Divide both sides by 4. Since 4 is positive, the inequality direction remains the same.

$$x<\frac{9}{4}$$