Question

Does each of these values of y make the inequality statement true or false? Complete the table.

y−3≥-5

y=−3

y=−2 (boundary)

y=−1

y − 3 ≥ −5

 

true

false

true

Answer 1

To determine whether each value of \(y\) makes the inequality statement \(y - 3 \geq -5\) true or false, let's evaluate the inequality for each value of \(y\).

1. **For \(y = -3\):**

\[
-3 - 3 \geq -5
\]
\[
-6 \geq -5 \quad \text{(False)}
\]

2. **For \(y = -2\) (boundary):**

\[
-2 - 3 \geq -5
\]
\[
-5 \geq -5 \quad \text{(True)}
\]

3. **For \(y = -1\):**

\[
-1 - 3 \geq -5
\]
\[
-4 \geq -5 \quad \text{(True)}
\]

Now, let's summarize the results in a table format:

| \(y\) | Inequality \(y - 3 \geq -5\) | True/False |
|:----------:|:-----------------------------:|:-------------:|
| \(-3\) | \(-6 \geq -5\) | False |
| \(-2\) | \(-5 \geq -5\) | True |
| \(-1\) | \(-4 \geq -5\) | True |

So, the completed table is:

- For \(y = -3\): **False**
- For \(y = -2\): **True**
- For \(y = -1\): **True**