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.)