Solve 8+2x/4<2*1-x/-2

$$\frac { 8 + 2 x } { 4 } < 2 \cdot \frac { 1 - x } { - 2 }$$

Solve for x

$$x>6$$

Solution Steps

Multiply both sides of the equation by 4, the least common multiple of 4,-2. Since 4 is positive, the inequality direction remains the same.

$$8+2x<-4\left(1-x\right)$$

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

$$8+2x<-4+4x$$

Subtract 4x from both sides.

$$8+2x-4x<-4$$

Combine 2x and -4x to get -2x.

$$8-2x<-4$$

Subtract 8 from both sides.

$$-2x<-4-8$$

Subtract 8 from -4 to get -12.

$$-2x<-12$$

Divide both sides by -2. Since -2 is negative, the inequality direction is changed.

$$x>\frac{-12}{-2}$$

Divide -12 by -2 to get 6.

$$x>6$$