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Writing Your Own Equations

The tables have been turned. Rather than solving an equation, you have to write the equation! This is a very simple piece of Algebra, and learning it can also assist in solving equations, since you are able to have a realistic scenario of the answer you are attempting to solve.

Here is an easy example:

1. Write an equation for the following statement: Three times a number is five less than 7.

Given a problem like this, you simply need to write down the equation that matches that statement.

Going left to right: Three times a number = 3X

Is 5 less than 7 = 7 - 5

Combine the two, and you have 3X = 7-5

Here is a table that contains many of the words and phrases, and how to express them mathematically:

Two times a number
Three times a number
(#) times a number
5 less than a number
12 less than a number
(#) less than a number
19 less than 39
(#1) less than (#2)
X - 5
X - 12
X - (#)
39 - 19
(#2) - (#1)
4 more than a number
7 more than 18
(#1) more than (#2)
The sum of 6 and a number
X + 4
18 + 7
(#1) + (#2)
X + 6

Using the above table as a reference, let's try a few:

1. Four times a number is four more than 16.
4X (four times a number)
= (is)
4 + 16 (four more than sixteen
Answer: 4X = 4 + 16

2. The sum of a number and two is equal to two times the number.
X + 2 (The sum of a number and two)
= (is equal to)
2X (two times the number)
Answer: X + 2 = 2X

3. Six dollars was three-quarters of the money we had.
6 (six)
= (was)
¾X (three-quarters of the money)
Answer: 6 = 3/4X
Note: Instead of the variable being called "a number," is "the money" in this example, which we can still rename to X.

Writing Inequalities
You can write inequalities exactly as shown above for equalities (standard equations), but instead of always having an equals sign, there will be greater than, less than, equals, or any combination of these signs. In these cases, when there is an "is" or "was" that may suggest that you need an equals sign, make sure there are no other keywords are immediately before or after it!

This table provides some common inequalities that you may encounter:

is greater than >
is less than <
is not greater than <= (less than or equal to)
is not less than >= (greater than or equal to)
is not equal to <> (also "!=" or "NOT =")
is not ! or "NOT"

Also note that you can change the symbol based on what you find easier. For example, if a problem says that "A number is not greater than 20," you could write it as: X !> 20 or X < = 20. Since if a number is not greater than 20, it must be less than or equal to 20!


Find another math lesson at the Math Lesson and Tutorial Center!


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