Question

Write the inequality , 3/2<x+1<7/2 in the modulus form

Answer 1

Given that

$\frac{3}{2}<x+1<\frac{7}{2} \newline \therefore\:\frac{3}{2}-1<x+1-1<\frac{7}{2}-1$

$\frac{1}{2}<x<\frac{5}{2}$

The range of x belong to (1/2 , 5/2).

Now,

$\qquad \frac{1}{2}<x<\frac{5}{2}\newline \therefore \quad \frac{1}{2}-\frac{3}{2}<x-\frac{3}{2}<\frac{5}{2}-\frac{3}{2} \newline \therefore \quad -1<x-\frac{3}{2}<1\newline \therefore \quad |x-\frac{3}{2}|<1$

Hence the given ineqaulity $\frac{3}{2}<x+1<\frac{7}{2}$ in the modulus form is $|x-\frac{3}{2}|<1$