Use the image to answer the question. Paolo solved an inequality and graphed the solution on the number line. Which of the following inequalities did he solve?
the line graph starts at -10 and ends at 10, the open circle is on 4, and the shaded line is facing -10.
Answers:
2.1x < 8.4
2.8x < 10.5
Unfortunately, as this is a text-based interface, I'm unable to view your image directly. However, based on your description, I can help you determine which inequality Paolo solved.
You described a number line that starts at -10 and ends at 10, with an open circle on 4, and the shaded line is facing towards -10. This indicates that Paolo solved an inequality where the solution set includes numbers that are less than 4 (but not including 4, because the circle at 4 is not filled in).
Now let's examine your answer choices:
1. 2.1x < 8.4
2. 2.8x < 10.5
To determine which inequality corresponds to the graph, we need to solve for x in each case:
1. 2.1x < 8.4
Divide both sides by 2.1 to solve for x:
x < 8.4 / 2.1
x < 4
2. 2.8x < 10.5
Divide both sides by 2.8 to solve for x:
x < 10.5 / 2.8
x < 3.75 (rounded to two decimal places)
Based on the graph description provided, the correct inequality is the one where the values of x are less than 4. Both inequalities provided result in solutions where x is less than 4, but only the first inequality, 2.1x < 8.4, has the exact boundary of x < 4, matching the description of the graph with an open circle at 4. This makes the first inequality (2.1x < 8.4) the most likely inequality Paolo solved and graphed.