Question

# Solve the following inequalities $\dfrac{{2x + 7}}{2} \leqslant 12,{\text{ x}} \in {\text{W}}$.

Hint- We need to solve the given inequality, but first let’s talk about the meaning of ${\text{x}} \in {\text{W}}$.This means that the value of x that will satisfy the given inequality should belong to set of whole numbers only. A whole number is one which is not a mixed fraction or any rational number, in fact these are just extended classes of natural numbers and they start with 0, 1, 2……………………..infinity.

Now let’s solve the given inequality $\dfrac{{2x + 7}}{2} \leqslant 12,{\text{ x}} \in {\text{W}}$
Let’s take the denominator part to the right hand side of the inequality we get
$2x + 7 \leqslant 24$
Now taking 7 to the right hand side of the equality we get
$\Rightarrow 2x \leqslant 17 \\ \Rightarrow x \leqslant \dfrac{{17}}{2} \\ \\$
Or $x \leqslant 8.5$………………. (1)
Now by the definition of whole numbers there are extended kinds of natural numbers which starts from 0 and goes up to infinity.
Now the value of x should be less than or equal to 8.5. However 8.5 is not a whole number thus the nearest whole number lesser than 8.5 is 8.
Thus the value of x is going from 0 to 8.
Hence the values of x satisfying the inequality $\dfrac{{2x + 7}}{2} \leqslant 12,{\text{ x}} \in {\text{W}}$ are 0, 1, 2, 3……..8.
Note – Whenever we face such type of problems the note point is to figure out what are the set of values of x being asked in the problem statement, just like in this case it was the set of whole numbers.