use the image to answer the 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 #
To determine which graph represents the solution to the inequality 12x−4<56, let's first solve the inequality:
\[ 12x - 4 < 56 \]
Add 4 to both sides to isolate the term with the variable x:
\[ 12x < 60 \]
Now, divide both sides by 12 to solve for x:
\[ x < 5 \]
The inequality \( x < 5 \) means that x can be any value less than 5, but not including 5 itself. Since it's a strict inequality (less than, not less than or equal), we're looking for a number line that has an open point at 5 and an arrow extending to the left, indicating all the numbers less than 5.
From the description given in the question, graph #2 fits this description. It has an open point marked on 5, and a leftward arrow that shows all the values less than 5.
Therefore, the correct answer is:
Graph #2.