Solve the inequality $3 (2 – x) \ge 2 (1 – x)$ for real $x$.

A man wants to cut three lengths from a single piece of board of length 91cm. The second length is to be 3cm longer than the shortest and the third length is to be twice as long as the shortest. What are the possible lengths of the shortest board if the third piece is to be at least 5cm longer than the second? [Hint: If $x$ is the length of the shortest board, then $x$, $(x + 3)$ and $2x$ are the lengths of the second and third piece, respectively. Thus, $x + (x + 3) + 2x \le 91$ and $2x \ge (x + 3) + 5$].

Solve the inequality $\frac{x}{4} < \frac{(5x-2)}{3} - \frac{(7x-3)}{5}$ for real $x$.

Solve $24x < 100$, when (ii) $x$ is an integer.

Solve the inequality $4x + 3 < 5x + 7$ for real $x$.

Solve $– 12x > 30$, when (i) $x$ is a natural number.

Solve $24x < 100$, when (i) $x$ is a natural number.

Find all pairs of consecutive odd positive integers both of which are smaller than 10 such that their sum is more than 11.

Solve the inequality $3x – 7 > 5x – 1$ for real $x$.

To receive Grade ‘A’ in a course, one must obtain an average of 90 marks or more in five examinations (each of 100 marks). If Sunita’s marks in first four examinations are 87, 92, 94 and 95, find minimum marks that Sunita must obtain in fifth examination to get grade ‘A’ in the course.

Solve the inequality $3(x – 1) \le 2 (x – 3)$ for real $x$.

Ravi obtained 70 and 75 marks in first two unit test. Find the minimum marks he should get in the third test to have an average of at least 60 marks.

Solve $3x + 8 > 2$, when (i) $x$ is an integer.

Solve the inequality $3 (1 – x) < 2 (x + 4)$ and show the graph of the solution on number line.

Solve $5x – 3 < 7$, when (ii) $x$ is a real number.

Solve the inequality $\frac{x}{3} > \frac{x}{2} + 1$ for real $x$.

Solve the inequality $5x – 3 > 3x – 5$ and show the graph of the solution on number line.

Solve the inequality $\frac{3(x-2)}{5} \le \frac{5(2-x)}{3}$ for real $x$.

Solve the inequality $3x – 2 < 2x + 1$ and show the graph of the solution on number line.

Solve $5x – 3 < 7$, when (i) $x$ is an integer.