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

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

Solve for x

$$x<-7$$

Solution Steps

Multiply both sides of the equation by 10, the least common multiple of 2,5. Since 10 is positive, the inequality direction remains the same.

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

Use the distributive property to multiply 5 by x+1.

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

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

$$5x+5<4x-2$$

Subtract 4x from both sides.

$$5x+5-4x<-2$$

Combine 5x and -4x to get x.

$$x+5<-2$$

Subtract 5 from both sides.

$$x<-2-5$$

Subtract 5 from -2 to get -7.

$$x<-7$$