Solve 3x-5/4-2x-1/5<-2

$$\frac { 3 x - 5 } { 4 } - \frac { 2 x - 1 } { 5 } < - 2$$

Solve for x

$$x<-\frac{19}{7}$$

Solution Steps

Multiply both sides of the equation by 20, the least common multiple of 4,5. Since 20 is positive, the inequality direction remains the same.

$$5\left(3x-5\right)-4\left(2x-1\right)<-40$$

Use the distributive property to multiply 5 by 3x-5.

$$15x-25-4\left(2x-1\right)<-40$$

Use the distributive property to multiply -4 by 2x-1.

$$15x-25-8x+4<-40$$

Combine 15x and -8x to get 7x.

$$7x-25+4<-40$$

Add -25 and 4 to get -21.

$$7x-21<-40$$

Add 21 to both sides.

$$7x<-40+21$$

Add -40 and 21 to get -19.

$$7x<-19$$

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

$$x<-\frac{19}{7}$$