Inequality Integers Eb2233

1. **Problem statement:** We are given two inequalities: a) $y \leq 7$ b) $y > -4.5$ For each, we need to find: (i) The largest or smallest integer $y$ could be. (ii) The list of integer values $y$ could take. (iii) Represent the inequality on a number line. --- ### Part a) $y \leq 7$ 2. **Step 1: Largest integer that $y$ could be** Since $y$ is less than or equal to 7, the largest integer $y$ can be is $7$ itself. 3. **Step 2: List of integer values $y$ could be** All integers less than or equal to 7 are possible values. This means: $$\ldots, 4, 5, 6, 7$$ 4. **Step 3: Represent inequality on number line** - Draw a number line. - Shade all points to the left of 7 including 7. - Mark 7 with a filled circle to show it is included. --- ### Part b) $y > -4.5$ 5. **Step 1: Smallest integer that $y$ could be** Since $y$ is strictly greater than $-4.5$, the smallest integer greater than $-4.5$ is $-4$. 6. **Step 2: List of integer values $y$ could be** All integers greater than $-4.5$ are: $$-4, -3, -2, -1, 0, 1, 2, \ldots$$ 7. **Step 3: Represent inequality on number line** - Draw a number line. - Shade all points to the right of $-4.5$. - Mark $-4.5$ with an open circle to show it is not included. - Mark integers starting from $-4$ and to the right. --- **Final answers:** a) (i) Largest integer $y$ could be: $7$ (ii) Integer values: $\ldots, 4, 5, 6, 7$ (iii) Number line with filled circle at $7$ and shading to the left. b) (i) Smallest integer $y$ could be: $-4$ (ii) Integer values: $-4, -3, -2, -1, 0, 1, 2, \ldots$ (iii) Number line with open circle at $-4.5$ and shading to the right.