How to Work with Inequalities

• 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.

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