GEEM - Teaching and Learning

C2.4 Solve inequalities that involve integers, and verify and graph the solutions.

Activity 1: Solving Inequalities

Solve the following inequalities, graph their solution on a number line, and then verify them.

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

Activity 2: Solving Inequalities

Solve the following inequality and graph the solution on a number line.

$3 x - 2 < 5 x + 5$

Step 1: Like an equation, I want to isolate the x's on one side of my inequality and the numbers on the other side to find the value of x. I understand that if I add an operation on one side of the inequality, I need to do the same thing on the other side of the inequality.

I understand that to isolate x, I have to divide -2x by -2. However, I have to do the same operation on the other side of the inequality. In this case, since I have to divide by a negative number, the sign of inequality changes.

$\begin{aligned} \frac{- 2 x}{- 2} & > \frac{6}{- 2} \\ x & > - 3 \end{aligned}$

The solutions are the numbers strictly greater than -3.

Step 2: I show the solutions graphically.

Source: translated from En avant, les maths!, 8^e année, CM, Algèbre, p. 3.

En avant, les maths!, 8^e année, CM, Algèbre, p. 3.