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 by 12: \[ x < 5 \]

This means that the solution includes all values of \( x \) that are less than 5.

Now, looking at the number lines:

• Graph 1: Has a closed point on 5 and includes numbers to the left (less than or equal to 5).
• Graph 2: Has an open point on 5 and includes numbers to the left (less than but not including 5).
• Graph 3: Has a closed point between 4 and 5 and includes numbers to the left (less than or equal to that point).
• Graph 4: Has an open point between 4 and 5 and includes numbers to the left (less than but not including that point).

Since our solution is \( x < 5 \) (not including 5), the graph that correctly represents this inequality is Graph 2, which has an open point on 5 and continues leftward.

Therefore, the answer is: Graph 2.