Which inequality represents the graph below:

Question

A number line is shown, the start of the number line starts on the number one and goes on the left side into the negative numbers, the circle is closed

(1 point)
Responses

3x−7≤−103 x minus 7 is less than or equal to negative 10

−3x−7≥−10negative 3 x minus 7 is greater than or equal to negative 10

−3x+7<10−3x+7<10

3x+7>10

Answer 1

Based on your description, the closed circle at 1 on the number line indicates that the inequality includes this value. Since the arrow goes to the left (indicating values less than or equal to 1), it suggests the inequality is "less than or equal to."

Out of the options you provided, you'll want to find the inequality that states "something is less than or equal to 1."

Now, we have the options:

1. \(3x - 7 \leq -10\)
2. \(-3x - 7 \geq -10\)
3. \(-3x + 7 < 10\)
4. \(3x + 7 > 10\)

Let's solve each of these inequalities to see which one would imply that \(x \leq 1\):

1. \(3x - 7 \leq -10\) → \(3x \leq -3\) → \(x \leq -1\)
2. \(-3x - 7 \geq -10\) → \(-3x \geq -3\) → \(x \leq 1\) (this one works)
3. \(-3x + 7 < 10\) → \(-3x < 3\) → \(x > -1\)
4. \(3x + 7 > 10\) → \(3x > 3\) → \(x > 1\)

Thus, the suitable inequality given your description of a closed circle at 1 that extends left is option 2: \(-3x - 7 \geq -10\).