Use the image to answer the question.

Question

Four number lines are shown labeled from 1 to 4 vertically one below the other. The number lines range from negative 10 to 10 with numbers listed in unit increments. The first number line has a closed point marked on 5. A leftward arrow is marked on the number line that originates at the closed point and goes beyond negative 10. The second number line has an open point marked on 5. A leftward arrow is marked on the number line that originates at the open point and goes beyond negative 10. The third number line has a closed point plotted on the number line between 4 and 5, just after the 4. A leftward arrow is marked on the number line that originates at the closed point and goes beyond negative 10. The fourth number line has an open point plotted on the number line between 4 and 5, just after the 4. A leftward arrow is marked on the number line that originates at the open point and goes beyond negative 10.

Which graph shows the solution to 12x−4<56
? Select 1, 2, 3, or 4 for your answer.

(1 point)

Answer 1

To solve the inequality \( 12x - 4 < 56 \), we first isolate \( x \).

1. Add 4 to both sides: \[ 12x < 56 + 4 \] \[ 12x < 60 \]

2. Divide both sides by 12: \[ x < \frac{60}{12} \] \[ x < 5 \]

This means \( x \) can take any value less than 5.

Now, we analyze the four number lines based on this solution:

1. Number Line 1: Closed point at 5 and a leftward arrow. This indicates \( x \leq 5\), which is not correct for our solution since \( x < 5\).

2. Number Line 2: Open point at 5 and a leftward arrow. This indicates \( x < 5\), which matches our solution.

3. Number Line 3: Closed point between 4 and 5, with a leftward arrow. This indicates \( x \leq 5\), which doesn't match our solution.

4. Number Line 4: Open point between 4 and 5, with a leftward arrow. This indicates \( x < 5\), but since it is between 4 and 5, it does not cover all values less than 5.

Thus, the correct graph that shows the solution to \( 12x - 4 < 56 \) is Number Line 2.

The answer is: 2.