Solve x/2+1<2left(x-1right)

$$\frac{ x }{ 2 } +1 < 2 \left( x-1 \right)$$

Solve for x

$$x>2$$

Solution Steps

Multiply both sides of the equation by 2. Since 2 is positive, the inequality direction remains the same.

$$x+2<4\left(x-1\right)$$

Use the distributive property to multiply 4 by x-1.

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

Subtract 4x from both sides.

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

Combine x and -4x to get -3x.

$$-3x+2<-4$$

Subtract 2 from both sides.

$$-3x<-4-2$$

Subtract 2 from -4 to get -6.

$$-3x<-6$$

Divide both sides by -3. Since -3 is negative, the inequality direction is changed.

$$x>\frac{-6}{-3}$$

Divide -6 by -3 to get 2.

$$x>2$$