Jitender Gupta and Divya Malik Solutions for Exercise 1: Topic Exercise

If the solution of the inequality $\text{2(2x + 3) -10 < 6(x-2)}$ for real $x$ is of the form $\left(k, \infty \right)$, then find the value of $k$.

If $P$ is the solution set of $-3\mathrm{x} + 4 < 2\mathrm{x} -3, \mathrm{x} \in \mathrm{N}$ and $Q$ is the solution set of $4\mathrm{x} -5 < 12, \mathrm{x} \in \mathrm{W}$, then $Q\cap P$ is $\left\{2, a, 4\right\}$. Find $a$

 If $\text{x∈R, }\left(a,\infty \right)$ is the solution of set $A$ of $\text{2(x -1) < 3x -1}$ and B is the solution set of $\text{ 4x -4 ≤ 8 + x}$, then $\text{A∪B}$ $=\left(-\infty ,\infty \right)$. Find $a$

Let $\mathrm{A}=\left\{\mathrm{x}: 11\mathrm{x}-5 >7\mathrm{x} +3,\mathrm{x}\in \mathrm{R}\right\} \mathrm{and} \mathrm{B}=\left\{\mathrm{x}: \mathrm{l} 8\mathrm{x} -9 \ge 15 + 12\mathrm{x}, \mathrm{x} \in \mathrm{R}\right\}$. Find $k$ where solution set of $\mathrm{A}\cap \mathrm{B}=\left(\mathrm{k}, \infty \right)$

Consider the given figure,

If the perimeter of triangle is less than equal to $33$ and greater than equal to $24$ Then, find the solution set, where $\mathrm{x}\in \mathrm{N}$.

One-third of a bamboo pole is buried in mud, one-sixth of it is in water and the part above the water is greater than or equal to $3$ units. Find the length of the shortest pole.

Find the greatest integer which is such that, if $7$ is added to its double, then the resulting number becomes greater than three times the integer.

The sum of three consecutive integers must not be more than $12$. What is the minimum positive integer?