Questions covered in Basic

Review the question prompts below before starting the timed test. Try each problem independently, then use the interactive test to record your answers and review the worked solutions.

1. The solution of the inequality $3x - 2 < 2x + 1$ is
2. If $-3x + 17 < -13$, then
3. The interval representing $x \ge -3$ and $x < 7$ is
4. The solution set of $|x| \le 5$ is
5. Which of the following is a strict inequality?
6. Solve the inequality $3(2-x) \ge 2(1-x)$.
7. Solve $4x + 3 < 6x + 7$.
8. Solve $\frac{x}{3} > \frac{x}{2} + 1$.
9. Solve the system of inequalities: $3x - 7 > 2(x - 6)$ and $6 - x > 11 - 2x$.
10. Solve the inequality graphically in two dimensional plane: $x + y < 5$.
11. Solve the following system of inequalities graphically: $x + 2y \le 8$, $2x + y \le 8$, $x \ge 0$, $y \ge 0$.
12. Case Study: Ravi obtained 70 and 75 marks in first two unit tests. He needs to maintain an average of at least 60 marks.
    (i) Let $x$ be the marks in the third test. Write the inequality representing the situation.
    (ii) Solve for $x$.
    (iii) If the maximum marks is 100, what is the range of marks Ravi can score?