Solve 6xleft(x-7right)<2left(3x-1right)left(x-8right)

$$6x \left( x-7 \right) < 2 \left( 3x-1 \right) \left( x-8 \right)$$

Solve for x

$$x<2$$

Solution Steps

Use the distributive property to multiply 6x by x-7.

$$6x^{2}-42x<2\left(3x-1\right)\left(x-8\right)$$

Use the distributive property to multiply 2 by 3x-1.

$$6x^{2}-42x<\left(6x-2\right)\left(x-8\right)$$

Use the distributive property to multiply 6x-2 by x-8 and combine like terms.

$$6x^{2}-42x<6x^{2}-50x+16$$

Subtract 6x^{2} from both sides.

$$6x^{2}-42x-6x^{2}<-50x+16$$

Combine 6x^{2} and -6x^{2} to get 0.

$$-42x<-50x+16$$

Add 50x to both sides.

$$-42x+50x<16$$

Combine -42x and 50x to get 8x.

$$8x<16$$

Divide both sides by 8. Since 8 is positive, the inequality direction remains the same.

$$x<\frac{16}{8}$$

Divide 16 by 8 to get 2.

$$x<2$$