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

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

Solve for r

$$r<-3$$

Solution Steps

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

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

Add 6 and 14 to get 20.

$$167<20-49r$$

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

$$20-49r>167$$

Subtract 20 from both sides.

$$-49r>167-20$$

Subtract 20 from 167 to get 147.

$$-49r>147$$

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

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

Divide 147 by -49 to get -3.

$$r<-3$$