Represent the following inequalities on a number line: a) -5/3 < x < -1/2 b) 1/2 x < 7/2

The inequality is approximately $-1.67 < x < -0.5$.

Mark integer points like $-2$, $-1$, and 0.

Since the inequalities are strict ($<$), use open circles at $-5/3$ and $-1/2$.

The number line representation is:

<--------------------------------------------------------------------->
-2             -5/3          -1/2             0               1
               o-------------o

(The line segment between the two open circles 'o' is shaded.)

The inequality is $0.5 \le x < 3.5$.

Mark integer points like 0, 1, 2, 3, and 4.

Since $x$ is greater than or equal to $1/2$ ($\le$), use a closed circle (solid dot) at $1/2$.
Since $x$ is strictly less than $7/2$ ($<$), use an open circle at $7/2$.

The number line representation is:

<--------------------------------------------------------------------->
0      1/2      1       2       3      7/2      4
       ●----------------------o

(The line segment between the closed circle '●' and the open circle 'o' is shaded.)