 How to Work with Inequalities - dummies

When numbers aren’t equal in value, you can’t use the equal sign (=) to turn them into an equation. Instead, you use a variety of other symbols to turn them into an inequality:

• The symbol > means is greater than, and the symbol < means is less than:

6 > 3 means 6 is greater than 3.

7 < 10 means 7 is less than 10.

If you’re not sure whether to use > or <, remember that the big open mouth of the symbol always faces the larger number. For example, 5 < 7, but 7 > 5.

• The following symbol means doesn’t equal: It’s not as useful as > or < because it doesn’t tell you whether a number is greater than or less than another number. Mostly, this symbol points out a mistake or inaccuracy in a pre-algebra calculation.

• The following symbol means approximately equals: You use it when you’re rounding numbers and estimating solutions to problems — that is, when you’re looking for an answer that’s close enough but not exact. This symbol allows you to make small adjustments to numbers to make your work easier.

## Sample questions

1. Place the correct symbol (=, >, or <) in the blank: 2 + 2 _______________ 5.

<. Because 2 + 2 = 4 and 4 is less than 5, use the symbol that means is less than.

2. Place the correct symbol (=, >, or <) in the blank: 42 – 19 _______________ 5 x 4.

>. Because 42 − 19 = 23 and 5 x 4 = 20, and 23 is greater than 20, use the symbol that means is greater than.

3. Sam worked 7 hours for his parents at \$8 an hour, and his parents paid him with a \$50 bill. Use the symbol doesn’t equal symbol to point out why Sam was upset. Sam worked 7 hours for \$8 an hour, so here’s how much he earned:

7 x \$8 = \$56

He was upset because his parents didn’t pay him the correct amount.

4. Find an approximate solution to 2,000,398 + 6,001, 756.

8,000,000. The two numbers are both in the millions, so you can use the approximate sign to round them to the nearest million: Now it’s easy to add 2,000,000 + 6,000,000 = 8,000,000.

## Practice questions

1. Place the correct symbol (=, >, or <) in the blanks:

a. 4 + 6 _______________ 13

b. 9 x 7 _______________ 62

c. 33 – 16 _______________ 60 / 3

d. 100 / 5 _______________ 83 – 63

2. Change the doesn’t equal signs to either > or <: 3. Tim’s boss paid him for 40 hours of work last week. Tim accounted for his time by saying that he spent 19 hours with clients, 11 hours driving, and 7 hours doing paperwork. Use the doesn’t equal symbol to show why Tim’s boss was unhappy with Tim’s work.

4. Find an approximate solution to 10,002 − 6,007.

Following are the answers for the practice questions:

1. a. 4 + 6 = 10, and 10 < 13

b. 9 x 7 = 63, and 63 > 62

c. 33 − 16 = 17 and 60 / 3 = 20, so 17 < 20.

d. 100 / 5 = 20 and 83 − 63, so 20 = 20.

2. a. 17 + 14 = 31, and 31 < 33

b. 144 − 90 = 54, and 54 < 66

c. 11 x 14 = 154, and 154 > 98

d. 150 / 6 = 25, and 25 > 20