GEEM - Teaching and Learning

C2.4 Solve inequalities that involve multiple terms and whole numbers, and verify and graph the solutions.

Activity 1: Solving Inequalities

Solve the inequalities below and graph their solution on a number line.

$5 x + 3 \leq 2 x + 18$

Sample Solution

Before I start solving this inequality, I need to check if I can collect like terms on each side. Then I will use the balance model to solve the inequality.

$\begin{aligned} 5 x + 3 & \leq 2 x + 18 \\ 5 x - 2 x + 3 & \leq 2 x - 2 x + 18 \\ 3 x + 3 - 3 & \leq 18 - 3 \\ 3 x & \leq 15 \\ \frac{3 x}{3} & \leq \frac{15}{3} \\ x & \leq 5 \end{aligned}$

The solutions are whole numbers less than or equal to 5. I can graph this solution on a number line by using a closed dot.

$5 x + 25 + x \geq 14 - 10 x - 7$

Sample Solution

To solve this inequality, I will first gather the like terms on each side. Then I will use the balance model to solve the inequality.

$\begin{aligned} 5 x - 25 + x & \geq 14 - 10 x - 7 \\ 5 x + x - 25 & \geq 14 - 7 - 10 x \\ 6 x - 25 & \geq 7 - 10 x \\ 6 x + 10 x - 25 & \geq 7 - 10 x + 10 x \\ 16 x - 25 + 25 & \geq 7 + 25 \\ 16 x & \geq 32 \\ \frac{16 x}{16} & \leq \frac{32}{16} \\ x & \geq 2 \end{aligned}$

The solutions are whole numbers greater than 2. I can graph this solution on a number line by using an open dot.

Source: translated from En avant, les maths!, 7^e année, CM, Algèbre, p. 3-5.

Activity 2: Inequalities

Solve the inequalities below. Graph their solution on a number line and then check them.

$4 x \leq - 6 x + 13 + 7$
$9 y - 3 y - 14 < 4$
$5 z - 2 \geq 3 z + 16$
$- 5 n > - 11 + 3 n - 5$