Algebra Know-It-ALL

624 Worked-Out Solutions to Exercises: Chapters 11 to 19

4. We are given the equation

x/3+x/6= 12

Multiplying through by 6, we get

6(x/3+x/6)= 72

When we apply the distributive law to the left side and then simplify the addends, we obtain

2 x+x= 72

Simplifying the left side further, we get

3 x= 72

Subtracting 72 from each side yields

3 x− 72 = 0

Finally, we can divide through by 3 to obtain lowest terms:

x− 24 = 0

5. When we have a first-degree equation in standard form, the solution process never takes
   more than two steps. Let’s solve the results of Probs. 1 through 4
   For Prob. 1 (Table B-1). The standard-form equation we got was

2 x+ 6 = 0

We subtract 6 from each side, getting

2 x=− 6

Table B-3. Solution to Prob. 3 in Chap. 12.

Statements Reasons

x− 7 = 7 x+x/7 This is the equation we are given

7(x− 7) = 7(7x+x/7) Multiply through by 7

7 x− 49 = 49 x+x Apply distributive law to each side

7 x− 49 = 50 x Simplify the right side

− 43 x− 49 = 0 Subtract 50x from each side

43 x+ 49 = 0 Multiply through by −1 and apply

the distributive law to the right side,

obtaining a more elegant equation