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)
Graph #

Answer 1

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

1. Add 4 to both sides:

   \[ 12x < 60 \]

2. Divide both sides by 12:

   \[ x < 5 \]

The solution \( x < 5 \) means we need to represent all numbers less than 5 on a number line.

• A closed point at 5 means that 5 is included in the solution; therefore, it does not represent \( x < 5\).
• An open point at 5 indicates that 5 is not included in the solution, which correctly represents \( x < 5\).

Among the provided number lines:

• Graph #1 has a closed point at 5, so it represents \( x \leq 5 \).
• Graph #2 has an open point at 5, showing \( x < 5 \).
• Graph #3 has a closed point between 4 and 5, indicating it includes that point.
• Graph #4 has an open point between 4 and 5, indicating it does not include that point.

Since we are looking for \( x < 5 \), the appropriate graph is:

Graph #2.