Idiot\'s Guides Basic Math and Pre-Algebra

Chapter 10: Solving Equations and Inequalities 123

Solving One-Step Equations

The simplest equations are the ones in which only one bit of arithmetic has been done to the

variable. If I tell you that I picked a number and added 4 and my answer was 9, you can figure

out what my number was by subtracting 4 from 9. If I pick a number, subtract 7 and get 15, you

can find my number by adding. In the same way, you can undo multiplying by dividing, and undo

division by multiplying. Let’s look at some examples.

Solve the equation x + 14 = 63

Because 14 was added to the original value of the variable to get 63, you want to subtract 14 to get

back to the original value. To keep the balance, subtract 14 from both sides. Subtracting 14 from

the left side leaves just x, and subtracting 14 from 63 tells you the value of the variable is 49.

To check your solution, write the original equation and replace the variable with the number you

found. If the result is a true statement, your solution is correct. In this case, x + 14 = 63 is the

original equation. You put your answer of 49 in place of x and you have 49 + 14 = 63, which is

true. The solution x = 49 is correct.

Here’s another example. This one asks you to undo subtraction.

Solve the equation x – 117 = 238

Someone took the number that x stands for and subtracted 117. When they were done, there was

238 left. To get back to the original value of x , you need to add 117 to both sides of the equation.

This will isolate x and give you 355 as the value of x.

You can check your solution by starting with x – 117 = 238 and putting 355 in place of x.

Because 355 – 117 = 238 is a true statement, you know your solution is correct.

Ready to try a multiplication equation? Solve the equation 19x = 28.5

Undo the multiplying by dividing. Divide both sides of the equation by 19.

Check your solution by replacing x in the original equation with 1.5. 19x = 28.5 becomes

19(1.5) = 28.5 and that’s true, so your solution is correct.

x

x

14 63

14 14

49

5 -

51

5

x

x

117 238

117 117

355









19 28 5

19

19

28 5

19

15

x

x

x

.

.

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