Idiot\'s Guides Basic Math and Pre-Algebra

126 Part 2: Into the Unknown

Are you ready for another example? This

one is a little different, just because the

order of the operations is a little different.

Solve y^7

3

5 - 15

2

In this case, the number represented by

y was reduced by 7—a subtraction was

performed. Then that result was divided by

3. So your plan should be first to multiply
   by 3, then to add 7.
   Multiplying both sides by 3 will eliminate
   the denominator.

Adding 7 to both sides will isolate y and tell

you the value of the variable.

Go back to the original equation to check

your solution.

y 7

3

5 - 15

2

becomes 38 7

3

515

• 
  

  (^2) - when
  you substitute -38 for y, and that is a true
  statement. The solution is correct.
  y
  y
  y
  7
  3
  15
  7
  3
  3153
  7455
  5?
  5

  
  


• 
  

(^2) -
2
(^2) -
y
y
745
77
538
511

25

WORLDLY WISDOM

A change in the order of things can sometimes make you feel confused about the solving

process. An equation that’s not in the order you’re used to seeing, like the equation

5 – 3x = 2 can cause some trouble. When you look at what’s happening in the equation,

it’s hard to know where to start and what happens in what order. Take a minute to

rewrite the equation 5 – 3x = 2 as -3x + 5 = 2. It will be easier to plan your solution.

Let’s look at one last example. This one can be solved two different ways. Let’s look at one

method here, and then we’ll tackle the other method in the next section.

Solve -3(x – 1) = -27

In this case, someone took for a number represented by x and subtracted 1 from it, then

multiplied the result by -3. In the original problem, the parentheses tell you to do the subtraction

first, then the multiplication. To solve the equation, you still want to do opposite operations in

the opposite order, so divide by -3 and then add 1.