Question

Find the values of x, which satisfy the inequation:

\(-2 \leq\ \frac{1}{2} - \frac{2x}{3} \leq\ \frac{11}{6}\) , x \(\epsilon\) N.

Answer 1

We have,

\(-2~\leq~(\frac{1}{2})~-~(\frac{2x}{3})~\leq~(\frac{11}{6})\)

\(-2~\leq~(\frac{1}{2})~-~(\frac{2x}{3})~\leq~(\frac{11}{6})\)

\(-12~\leq~3-4x~\leq~11\)

\(\Rightarrow~-12~-3~\leq~3~-~4x~-~3~\leq~11~-~3\)

\(-15~\leq~-4x~\leq~ 8\)

\(15~\geq~4x~\geq~-8\)

\(-8 ~\leq~4x~\leq~15\)

\(-2~\leq~x~\leq~(\frac{15}{4})\)

\(-2~\leq~x~\leq~3(\frac{3}{4})\)

But, \(x~\epsilon~ N\) , i.e \(x~\epsilon~\){1,2,3,4,….}

So, the solution set is {1,2,3}.