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

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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.

Complete step-by-step answer:

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.

This will help you reach the right answer for the required values of x.

Complete step-by-step answer:

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.

This will help you reach the right answer for the required values of x.

Last updated date: 23rd Sep 2023

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