Solve 167<6+7(2-7x)

$$167 < 6 + 7 ( 2 - 7 x )$$

Solve for x

$$x<-3$$

Solution Steps

Use the distributive property to multiply 7 by 2-7x.

$$167<6+14-49x$$

Add 6 and 14 to get 20.

$$167<20-49x$$

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

$$20-49x>167$$

Subtract 20 from both sides.

$$-49x>167-20$$

Subtract 20 from 167 to get 147.

$$-49x>147$$

Divide both sides by -49. Since -49 is negative, the inequality direction is changed.

$$x<\frac{147}{-49}$$

Divide 147 by -49 to get -3.

$$x<-3$$