Solve x-1/2-2<3x-2/5

$$\frac { x - 1 } { 2 } - 2 < \frac { 3 x - 2 } { 5 }$$

Solve for x

$$x>-21$$

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.

$$5\left(x-1\right)-20<2\left(3x-2\right)$$

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

$$5x-5-20<2\left(3x-2\right)$$

Subtract 20 from -5 to get -25.

$$5x-25<2\left(3x-2\right)$$

Use the distributive property to multiply 2 by 3x-2.

$$5x-25<6x-4$$

Subtract 6x from both sides.

$$5x-25-6x<-4$$

Combine 5x and -6x to get -x.

$$-x-25<-4$$

Add 25 to both sides.

$$-x<-4+25$$

Add -4 and 25 to get 21.

$$-x<21$$

Divide both sides by -1. Since -1 is negative, the inequality direction is changed.

$$x>-21$$