Question

Show that if 5/3< 2x< 11/3, then x∈{y∈R such that |y- 4/3| < 1/2}

Answer 1

$$5/3<2x<11/3\\ 5/6<x<11/6$$

$$|y- 4/3| < 1/2\\ -1/2<y- 4/3<1/2\\ -1/2+4/3<y<1/2+4/3\\ 5/6<y<11/6$$

so $x\in \{ y\in R: |y-\frac{4}{3}|<\frac{1}{2}\}$