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

Last updated date: 10th Aug 2024
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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.

Now let’s solve the given inequality $\dfrac{{2x + 7}}{2} \leqslant 12,{\text{ x}} \in {\text{W}}$
$2x + 7 \leqslant 24$
$\Rightarrow 2x \leqslant 17 \\ \Rightarrow x \leqslant \dfrac{{17}}{2} \\ \\$
Or $x \leqslant 8.5$………………. (1)
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.