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.
- 4x + 6x ≤ 13 + 7
- 9y - 3y < 14 + 4
- 5z - 2 ≥ 3z + 16
- 11 - 5n > 3n - 5n
Activity 2: Solving Inequalities
Solve the following inequality and graph the solution on a number line.
3x - 2 < 5x + 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.
\(\begin{align} \frac{-2x}{-2} &> \frac{6}{-2} \\ x &> -3 \end{align}\)
The solutions are the numbers greater than -3.
Step 2: I show the solutions graphically.
Source: En avant, les maths!, 8e année, CM, Algèbre, p. 3.