Solve x-x/2+x+1/3<1+x+8/6

$$x- \frac{ x }{ 2 } + \frac{ x+1 }{ 3 } < 1+ \frac{ x+8 }{ 6 }$$

Solve for x

$$x<3$$

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.

$$6x-3x+2\left(x+1\right)<6+x+8$$

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

$$3x+2\left(x+1\right)<6+x+8$$

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

$$3x+2x+2<6+x+8$$

Combine 3x and 2x to get 5x.

$$5x+2<6+x+8$$

Add 6 and 8 to get 14.

$$5x+2<14+x$$

Subtract x from both sides.

$$5x+2-x<14$$

Combine 5x and -x to get 4x.

$$4x+2<14$$

Subtract 2 from both sides.

$$4x<14-2$$

Subtract 2 from 14 to get 12.

$$4x<12$$

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

$$x<\frac{12}{4}$$

Divide 12 by 4 to get 3.

$$x<3$$