Topics 5: Inequalities and Regions – Sample Activity

Context

Anarika, a university student, has seen three pairs of bedsheets she likes. They cost UGX 225,000, UGX 247,500 and UGX 306,000. She has already saved UGX 90,000 and gets UGX 18,000 pocket money per week at the end of each week. Anarika is wondering how soon she can buy one of these pairs of bedsheets.

Support Material

Task

Write a plan to advise Anarika on the different methods she can you use to help her solve this problem.

Topic Summary

In this topic, you have learnt that:

·when we write inequalities, we use special symbols to show the relationship between the numbers in them.

• for the inequality greater than/less than sign, conventionally use an unshaded circle/empty circle.
• for the inequality less than/ greater than or equal to sign, conventionally use a shaded circle/solid dot
• to graph a linear inequality:
  • Identify and graph the boundary line. If the inequality is <, > the boundary line is solid. If the inequality is < or>, the boundary line is dashed/dotted.
  • Test a point that is not on the boundary line to establish if it is a solution of the inequality.
  • Shade out one side of the boundary line. If the test point is a solution, shade out the side that includes the point. If the test point is not a solution, shade out the opposite side.

Extended tasks

1. Write the following statements using inequalities.

(a) Haruna (A) is taller than Hilder (D) by 5 cm.

(b) The width (W) of the room is less than of the length (L) by 8 metres.

(c) The house (h) is at most worth than UGX 5 million.

(d) The distance between Jinja and Kampala is between 60 km and 90 km.

2. Show on a number line the following inequalities.

(a) T = {t: t≤6}

(b) M={t: tz-6}

(c) R = {t: t>-5}

(d) Q = {t: -3 st≤5}

(e) E = The numbers different from 4 indicated by the inequality, {x: x = 4)

3. Write down the values of t for which the following inequality is true.

2(3-t) 4-ts9-2t

4. In a school, the number of girls is 60 more than twice the number of boys enrolled.

Given that the number of learners at the school is at most 680, determine the greatest possible number of girls and the greatest number of boys at the school. Show the region satisfied by the inequalities.