Question

Solve- $4x - 6x \leqslant 7 - 3 - 2x \leqslant 4$ when $x$ is an integer.

Answer 1

In the given problem, we are asked to solve the equation, since we have one variable it is easy to solve the given equations. We have to find the value of $x$. By using the simple concept on the inequalities, which is $\geqslant$ a symbol of greater or equals to sign and $\leqslant$ a symbol of less than equals to sign, which means it is either less than the given values or equals to the given values.

Complete step by step answer:
Since given that the equation
$4x - 6x \leqslant 7 - 3 - 2x \leqslant 4$ and then we need to find the value of the unknown variable $x$ for the integer number systems, so we will make use of the basic mathematical operations to simplify further.
Now Turing the variables on the left-hand side and also the numbers on the right-hand side we get $4x - 6x \leqslant 7 - 3$ while changing the values on the equals to, the sign of the values or the numbers will change.
Hence by the addition and subtraction operation, we have, $4x - 6x \leqslant 7 - 3 \Rightarrow - 2x \geqslant 4$
Thus, by division, we get $- 2x \geqslant 4 \Rightarrow x \geqslant \dfrac{{ - 4}}{2} \Rightarrow x \geqslant - 2$
Hence, we have the values as $x \geqslant - 2$
Since the unknown variable $x$ is given as integer, which means Natural numbers are $\\{ 1,2,3,...\infty \\}$ and whole numbers defined as $\\{ 0,1,2,3,...\infty \\}$ and integers defined as $\\{ - \infty ,..., - 3, - 2, - 1,0,1,2,3,...\infty \\}$ and the rational and irrational also, hence integers numbers means all should be contained in them, they $x \geqslant - 2$ can be expressed as a integer form of $x \in ( - 2,\infty )$ where the number $2$ is at least.

Note:
In the above steps while using the concepts on the inequalities which is the less than or equal to (or) greater than equal to, we might make mistakes when applying it, so learn the concept well.
The other two operations are multiplication and division operations. Since multiplicand refers to the number multiplied. Also, a multiplier refers that multiplies the first number. Have a look at an example; while multiplying $5 \times 7$the number $5$ is called the multiplicand and $- 4x \geqslant - 8 \Rightarrow 4x \leqslant 8 \Rightarrow$the number $7$ is called the multiplier. Like $2 \times 3 = 6$ or which can be also expressed in the form of $2 + 2 + 2(3times)$
The process of the inverse of multiplication method is called division. Like $x \times y = z$is multiplication thus the division sees as $x = \dfrac{z}{y}$. Like $4x \leqslant 8 \Rightarrow x \leqslant \dfrac{8}{4} \Rightarrow x \leqslant 2$
Hence using simple operations, we solved the given problem.