Question

If $x = 4,5,6$, then which among the following options is correct.
A) $x \geqslant 4$ and $x \leqslant 7$
B) $x \geqslant 4$ and $x < 7$
C) $x > 4$ and $x < 7$
D) $x > 4$ and $x \leqslant 7$

Answer 1

Hint: First check all the options and write the possible solutions for all the options. Later we must check which among the options match with the solution set given in the question.

Complete step-by-step answer:
The option (A) is $x \geqslant 4$ and $x \leqslant 7$.
Now, find the solution for x,
The solution for $x \geqslant 4$ is $\left\{ {4,5,6,7, \ldots } \right\}$.
The solution for $x \leqslant 7$ is $\left\{ { \ldots ,5,6,7} \right\}$.
So, the solution of $x \geqslant 4$ and $x \leqslant 7$ is $\left\{ {4,5,6,7} \right\}$.
The value of $x$ in option (A) doesn’t match the given value of $x$.
The option (B) is $x \geqslant 4$ and $x < 7$.
Now, find the solution for x,
The solution for $x \geqslant 4$ is $\left\{ {4,5,6,7, \ldots } \right\}$.
The solution for $x < 7$ is $\left\{ { \ldots ,3,4,5,6} \right\}$.
So, the solution of $x \geqslant 4$ and $x < 7$ is $\left\{ {4,5,6} \right\}$.
The value of $x$ in option (B) is the same as the given value of $x$.
The option (C) is $x > 4$ and $x < 7$.
Now, find the solution for x,
The solution for $x > 4$ is $\left\{ {5,6,7, \ldots } \right\}$.
The solution for $x < 7$ is $\left\{ { \ldots ,3,4,5,6} \right\}$.
So, the solution of $x > 4$ and $x < 7$ is $\left\{ {5,6} \right\}$.
The value of $x$ in option (C) doesn’t match the given value of $x$.
The option (D) is $x > 4$ and $x \leqslant 7$.
Now, find the solution for x,
The solution for $x > 4$ is $\left\{ {5,6,7, \ldots } \right\}$.
The solution for $x \leqslant 7$ is $\left\{ { \ldots ,5,6,7} \right\}$.
So, the solution of $x > 4$ and $x \leqslant 7$ is $\left\{ {5,6,7} \right\}$.
The value of $x$ in option (D) doesn’t match the given value of $x$.

Hence, option (B) is correct.

Note: Linear Inequalities can be explained as an inequality (represented by the symbols of inequality) that holds a linear function. A linear function can be described as any function whose graph is a straight line. Now, if you are wondering what inequality means in the field of Mathematics. Here is your answer. When two real numbers or two algebraic expressions are represented with symbols like $<$, $>$ or $\leqslant$, $\geqslant$ they can be called an inequality.