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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 answer

To solve the inequality \( 12x - 4 < 56 \), we can start by isolating \( x \).

  1. Add 4 to both sides: \[ 12x < 60 \]

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

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

Now, we need to identify which of the number lines illustrates this solution.

  • Number Line 1: Has a closed point at 5 and indicates values less than or equal to 5. (This is not the correct solution since \( x < 5 \) does not include 5.)
  • Number Line 2: Has an open point at 5 and includes values less than 5. (This is correct as it reflects \( x < 5 \).)
  • Number Line 3: Has a closed point just after 4 and indicates values less than or equal to that point (again not including values down to negative but limits them, which is incorrect since we are only interested in values less than 5).
  • Number Line 4: Has an open point just after 4 and includes values less than that point (also does not depict the correct solution as it does not extend to less than 5).

The graph that correctly shows the solution to \( 12x - 4 < 56\) is the second number line, which represents \( x < 5 \) with an open point. Thus the answer is:

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