Solve 42>6(b-2)-6(1-4b)

$$42 > 6 ( b - 2 ) - 6 ( 1 - 4 b )$$

Solve for b

$$b<2$$

Solution Steps

Use the distributive property to multiply 6 by b-2.

$$42>6b-12-6\left(1-4b\right)$$

Use the distributive property to multiply -6 by 1-4b.

$$42>6b-12-6+24b$$

Subtract 6 from -12 to get -18.

$$42>6b-18+24b$$

Combine 6b and 24b to get 30b.

$$42>30b-18$$

Swap sides so that all variable terms are on the left hand side. This changes the sign direction.

$$30b-18<42$$

Add 18 to both sides.

$$30b<42+18$$

Add 42 and 18 to get 60.

$$30b<60$$

Divide both sides by 30. Since 30 is positive, the inequality direction remains the same.

$$b<\frac{60}{30}$$

Divide 60 by 30 to get 2.

$$b<2$$