Represent each inequality on a number line. 4. $$ x5-1 $$ 6. $$ y \geq-4 $$

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Represent each inequality on a number line. 4. $$ x>5>-1 $$ 6. $$ y \geq-4 $$

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To represent the inequalities on a number line, we will analyze each inequality step by step. ### Inequality 4: $$ x > 5 > -1 $$ This inequality can be broken down into two parts: 1. $$ x > 5 $$ 2. $$ 5 > -1 $$ (which is always true) The relevant part for the number line is $$ x > 5 $$. This means that $$ x $$ can take any value greater than 5. **Representation on the number line:** - We will draw an open circle at 5 (indicating that 5 is not included). - We will shade the line to the right of 5 to indicate all values greater than 5. ### Inequality 6: $$ y \geq -4 $$ This inequality states that $$ y $$ is greater than or equal to -4. **Representation on the number line:** - We will draw a closed circle at -4 (indicating that -4 is included). - We will shade the line to the right of -4 to indicate all values greater than or equal to -4. ### Summary of Representations: 1. For $$ x > 5 $$: - Open circle at 5, shading to the right. 2. For $$ y \geq -4 $$: - Closed circle at -4, shading to the right. These representations can be visualized on a number line as follows: ``` Number Line for x > 5: <---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---> -2 -1 0 1 2 3 4 5 6 7 8 9 10 (---------------------> Number Line for y ≥ -4: <---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---> -6 -5 -4 -3 -2 -1 0 1 2 3 4 ●---------------------> ``` In the above representation: - The open circle at 5 indicates that 5 is not included in the solution for $$ x $$. - The closed circle at -4 indicates that -4 is included in the solution for $$ y $$. To represent the inequalities on a number line: 1. **For $$ x > 5 $$:** - Draw an open circle at 5. - Shade the line to the right of 5. 2. **For $$ y \geq -4 $$:** - Draw a closed circle at -4. - Shade the line to the right of -4. These representations show all values greater than 5 for $$ x $$ and all values greater than or equal to -4 for $$ y $$.

Represent each inequality on a number line. 4. \( x>5>-1 \) 6. \( y \geq-4 \)

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