Solve 1+x+1/2>1/3(1-2x)

$$1+ \frac{ x+1 }{ 2 } > \frac{ 1 }{ 3 } (1-2x)$$

Solve for x

$$x>-1$$

Solution Steps

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

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

Use the distributive property to multiply 3 by x+1.

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

Add 6 and 3 to get 9.

$$9+3x>2\left(1-2x\right)$$

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

$$9+3x>2-4x$$

Add 4x to both sides.

$$9+3x+4x>2$$

Combine 3x and 4x to get 7x.

$$9+7x>2$$

Subtract 9 from both sides.

$$7x>2-9$$

Subtract 9 from 2 to get -7.

$$7x>-7$$

Divide both sides by 7. Since 7 is positive, the inequality direction remains the same.

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

Divide -7 by 7 to get -1.

$$x>-1$$