GEEM - Teaching and Learning

C2.4 Solve inequalities that involve two operations and whole numbers up to 100 and verify and graph the solutions.

Activity 1: Solving an Inequality Including the Equal Sign

Ask students to solve the inequality $ 5x + 50 \leq 100 $ and represent their solution using a number line.

Strategy

Represent this Inequality Using a Number Line

First I need to isolate the variable x.

5 “x”, plus, 50, smaller or equal to 100. 5 “x”, plus, 50 – 50, smaller or equal to 100, minus 50.5 “x” smaller or equal to 50.5 “x” smaller or equal to 50, divided both factors by 5.“x” smaller or equal to 10.

Since the equation includes the equal sign, I can draw a closed dot on the number 10 with the line arrowed to the left to show the results "all numbers less than or equal to 10".

Number line with number one to 20. A dot is marked on number 10 and an arrow goes left until number one.

The possible values of x are the whole numbers less than or equal to 10, namely 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 and 0.

Source : En avant, les maths!, 6^e année, CM, Algèbre, p. 3.

Activity 2: Solving an Inequality Involving "Less Than" or "Greater Than"

Have students solve the inequality $2m + 38 < 90$ and represent their solution with a number line.

Strategy

Represent Solutions Using a Number Line

To represent this inequality on a number line, I first need to isolate the variable m.

2 “m”, plus, 38, greater than 90.2“m“, plus, 38, minus 38, greater than 90, minus 38.2 “m” greater than 52.2 “m” greater than 52, divided both factors by two. “m” greater than 26.

Number line with numbers of 21 to 40. A point is on number 26 and an arrow points right from number 26 to 35.

I draw a line and use the open dot, on the number 26, to indicate that the inequality relation is "greater than" 26. The possible values of m are the whole numbers greater than 26, namely 27, 28, 29, etc.

Source : En avant, les maths!, 6^e année, CM, Algèbre, p. 4.

Activity 3: Working to Spoil Yourself!

Present students with the following problem:

Erykah found three pairs of running shoes that she likes, costing $50, $59 and $79 respectively. She has already saved $31. She works for a dog walking service that pays her $15 per hour. How many hours will she have to work to buy any of these pairs of shoes? Represent your solution on a number line.

Encourage students to work in teams to solve the problem.

Example

Represent the problem algebraically using an inequality:

Erykah earns $15 x h, where h is the number of hours worked.

The first pair of shoes costs $50, and Erykah has already saved $31. So, to buy these shoes, Erykah must have $50 - $31.

To find the number of hours Erykah will have to work to buy the first pair of shoes, the algebraic inequality is:

15 x h ≥ 50 - 31

15 x h ≥ 19

h	15 x h	≥ 19
0	0	no
1	15	no
2	30	yes
3	45	yes

15 x h ≥ 19

15 x 2 ≥ 19

Erykah has to work 2 hours.

Ask a few teams to present their solution. Allow students to review their answer.