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

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

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

Solve the inequality $37 – (3x + 5) > 9x – 8 (x – 3)$ for real $x$.

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

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

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

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

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

Solve the inequality $2 (2x + 3) – 10 < 6 (x – 2)$ for real $x$.

Find all pairs of consecutive even positive integers, both of which are larger than 5 such that their sum is less than 23.

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

Solve the inequality $x + \frac{x}{2} + \frac{x}{3} < 11$ for real $x$.

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

The longest side of a triangle is 3 times the shortest side and the third side is 2 cm shorter than the longest side. If the perimeter of the triangle is at least 61 cm, find the minimum length of the shortest side.

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

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 $3x + 8 > 2$, when (ii) $x$ is a real number.

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