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: \[ 12x < 56 + 4 \] \[ 12x < 60 \]

2. Divide both sides by 12: \[ x < 5 \]

The solution to the inequality is \( x < 5 \).

Now, we need to identify which graph represents this solution. We look for a graph that has an open point on 5 (indicating that 5 is not included in the solution) and an arrow extending to the left (indicating all numbers less than 5).

Given the descriptions of the graphs:

1. Graph 1: Closed point at 5, arrow leftward (includes 5) - not the solution.
2. Graph 2: Open point at 5, arrow leftward - this matches \( x < 5 \).
3. Graph 3: Closed point between 4 and 5, arrow leftward (includes point > 4) - not the solution.
4. Graph 4: Open point between 4 and 5, arrow leftward - not the complete representation of \( x < 5 \).

Thus, the correct answer is Graph 2.