A) Represent -5/3 < x < -1/2 on a number line.

Here are the number line representations for the given inequalities:

a) Represent $-5/3 < x < -1/2$ on a number line.

First, convert the fractions to decimals for easier placement:
$-5/3 \approx -1.67$
$-1/2 = -0.5$
So the inequality is approximately $-1.67 < x < -0.5$.

To represent this on a number line:

1. Draw a horizontal line and label it as a number line.
2. Mark key integer points like $-2$, $-1$, and 0.
3. Locate $-5/3$ (between $-2$ and $-1$, closer to $-1.5$) and $-1/2$ (between $-1$ and 0).
4. Place an open circle at $-5/3$ because $x$ is strictly greater than $-5/3$ (not equal to).
5. Place an open circle at $-1/2$ because $x$ is strictly less than $-1/2$ (not equal to).
6. Shade the region between the two open circles to indicate all values of $x$ that satisfy the inequality.

The number line representation would look like this:

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

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

b) Represent $1/2 \le x < 7/2$ on a number line.

First, convert the fractions to decimals for easier placement:
$1/2 = 0.5$
$7/2 = 3.5$
So the inequality is $0.5 \le x < 3.5$.

To represent this on a number line:

1. Draw a horizontal line and label it as a number line.
2. Mark key integer points like 0, 1, 2, 3, and 4.
3. Locate $1/2$ (between 0 and 1) and $7/2$ (between 3 and 4).
4. Place a closed circle (or solid dot) at $1/2$ because $x$ is greater than or equal to $1/2$.
5. Place an open circle at $7/2$ because $x$ is strictly less than $7/2$ (not equal to).
6. Shade the region between the closed circle at $1/2$ and the open circle at $7/2$ to indicate all values of $x$ that satisfy the inequality.

The number line representation would look like this:

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

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