Algebra Know-It-ALL

If we add 18z to each side, we get

z+ 18 z≥− 18 z− 18 + 18 z

which simplifies to

19 z≥− 18

We finish by dividing each side by 19. That leaves us with

z≥−18/19

The original inequality holds true for all values of z larger than or equal to −18/19.

Chapter 12

1. See Table B-1.


2. See Table B-2.


3. See Table B-3.

Table B-2. Solution to Prob. 2 in Chap. 12.

Statements Reasons

x/3= 6 x+ 2 This is the equation we are given

x= 3(6x+ 2) Multiply through by 3

x= 18 x+ 6 Distributive law applied to the right side

− 17 x= 6 Subtract 18x from each side

− 17 x− 6 = 0 Subtract 6 from each side

17 x+ 6 = 0 Multiply through by −1 and apply

the distributive law to the right side,

obtaining a more elegant equation

Chapter 12 623

Table B-1. Solution to Prob. 1 in Chap. 12.

Statements Reasons

4x+ 4 = 2x − 2 This is the equation we are given

2 x+ 4 =−2 Subtract 2 x from each side

2 x+ 6 = 0 Add 2 to each side