Solve 21x(x-7)<3(7x-1)(x-8)

$$21 x ( x - 7 ) < 3 ( 7 x - 1 ) ( x - 8 )$$

Solve for x

$$x<1$$

Solution Steps

Use the distributive property to multiply 21x by x-7.

$$21x^{2}-147x<3\left(7x-1\right)\left(x-8\right)$$

Use the distributive property to multiply 3 by 7x-1.

$$21x^{2}-147x<\left(21x-3\right)\left(x-8\right)$$

Use the distributive property to multiply 21x-3 by x-8 and combine like terms.

$$21x^{2}-147x<21x^{2}-171x+24$$

Subtract 21x^{2} from both sides.

$$21x^{2}-147x-21x^{2}<-171x+24$$

Combine 21x^{2} and -21x^{2} to get 0.

$$-147x<-171x+24$$

Add 171x to both sides.

$$-147x+171x<24$$

Combine -147x and 171x to get 24x.

$$24x<24$$

Divide both sides by 24. Since 24 is positive, the inequality direction remains the same.

$$x<\frac{24}{24}$$

Divide 24 by 24 to get 1.

$$x<1$$