9.7.1 Working Out Inequalities

Activity Symbol Activity: Inequalities

For this activity, you should write your answers to the prompts on a separate sheet of paper. Once you are finished, compare your answers to the answers here. Don't worry if your wording does not match exactly.

(a) Place the correct symbol ( < or > ) in the blank spaces below.

  • (i) 4 __ 7

  • (ii) 18 __ 10

  • (iii) 3 __ two minus

Hint symbol

Comment

Write the inequality using words first and then convert this to the correct symbol.

Answer Symbol

Answer

(a) Compare your answers to the correct answers here.

  • (i) 4 < 7

  • (ii) 18 > 10

  • (iii) 3 > two minus

(b) Evaluate what the following mathematical statements mean. Write your answers as full sentences.

  • (i) Balance in account > 0.

  • (ii) Speed (in mph) on highway ≤ 65.

  • (iii) 18 ≤ age (in years) ≤ 50.

Answer Symbol

Answer

(b) Compare the answers you wrote down to the correct answers here. They may be worded differently, so make sure that they have the same meaning.

  • (i) The balance in the account is greater than zero, so there is credit in the account.

  • (ii) The speed on the highway is less than or equal to 65 miles per hour.

  • (iii) The age in years is between 18 and 50, inclusively.

(c) Rewrite the following sentences as statements using the inequality symbols.

  • (i) The refrigerator temperature should be less than 40°F.

  • (ii) There must be at least five people on the committee.

  • (iii) For an ideal weight, a person’s BMI should be greater than 20 and less than 25.

Answer Symbol

Answer

(c) Compare the answers you wrote down to the correct answers here. They may be worded differently, so make sure that they have the same meaning.

  • (i) Refrigerator temperature (in ºF) < 40.

  • (ii) Number of people on committee ≥ 5.

  • (iii) 20 < BMI < 25

Inequalities are also used in computer programs to check whether conditions have been fulfilled. For example, if the balance in your bank account is negative, you may be prevented from withdrawing money from a cash machine.

Video clip iconThe more practice you can get at inequalities, the easier they will get so try out this game [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)] .

9.7 Writing Inequalities

9.8 An Unsolved Problem!