Solve 6(3x+1)-2(5x-4)<5(x+2)

$$6 ( 3 x + 1 ) - 2 ( 5 x - 4 ) < 5 ( x + 2 )$$

Solve for x

$$x<-\frac{4}{3}$$

Solution Steps

Use the distributive property to multiply 6 by 3x+1.

$$18x+6-2\left(5x-4\right)<5\left(x+2\right)$$

Use the distributive property to multiply -2 by 5x-4.

$$18x+6-10x+8<5\left(x+2\right)$$

Combine 18x and -10x to get 8x.

$$8x+6+8<5\left(x+2\right)$$

Add 6 and 8 to get 14.

$$8x+14<5\left(x+2\right)$$

Use the distributive property to multiply 5 by x+2.

$$8x+14<5x+10$$

Subtract 5x from both sides.

$$8x+14-5x<10$$

Combine 8x and -5x to get 3x.

$$3x+14<10$$

Subtract 14 from both sides.

$$3x<10-14$$

Subtract 14 from 10 to get -4.

$$3x<-4$$

Divide both sides by 3. Since 3 is positive, the inequality direction remains the same.

$$x<-\frac{4}{3}$$