Graph the compound inequality on the number line.

x>-6 and x≤7

1 answer

To graph the compound inequality \( x > -6 \) and \( x \leq 7 \) on a number line, follow these steps:

  1. Identify the interval for \( x > -6 \):

    • This means that \( x \) can take any value greater than -6. The boundary -6 is not included, so we use an open circle at -6.
    • The graph will extend to the right, indicating all values greater than -6.
  2. Identify the interval for \( x \leq 7 \):

    • This means that \( x \) can take any value less than or equal to 7. The boundary 7 is included, so we use a closed circle at 7.
    • The graph will extend to the left, indicating all values less than or equal to 7.
  3. Combine both intervals:

    • Since the inequalities must be satisfied simultaneously, we focus on the overlapping region between the two intervals, which is from just above -6 to 7.

Now, here's how you can represent this graphically on a number line:

<----(-----●==================●-----)---->
      -6                   7
  • The open circle ( ) at -6 means that -6 is not included.
  • The closed circle (●) at 7 means that 7 is included.
  • The line between -6 and 7, indicated by the equals sign (=), shows all the values that are included in the solution.

Thus, the solution for the compound inequality \( x > -6 \) and \( x \leq 7 \) on the number line is represented by the interval (-6, 7].