Solve for x and graph the solution on the number line below. -64›8x. Make sure to include how to shade the number line and include the inequality notion

Answer 1

To solve the inequality \(-64 > 8x\), we can follow these steps:

1. Isolate the variable \(x\): We want to solve for \(x\) by dividing both sides of the inequality by 8.

   \[ \frac{-64}{8} > x \] \[ -8 > x \]

   This can also be rewritten as: \[ x < -8 \]

2. Graph the solution on a number line: To represent the solution \(x < -8\) on a number line:

   • Draw a number line with a range that clearly includes the number -8.
   • Use an open circle at -8 to indicate that -8 is not included in the solution (because the inequality is strictly less than).
   • Shade the line to the left of -8 to indicate all numbers less than -8 are included in the solution.

Here’s an example of how the number line would look:

<---|----|----|----|----|----|----|----|----|----|--->
    -10   -9   -8   -7   -6   -5   -4   -3   -2
             O
<----------------

• In the graph:
  • O at -8 is an open circle, indicating that -8 is not part of the solution.
  • The shading to the left indicates that all values less than -8 satisfy the inequality.

Thus, the solution to the inequality \(-64 > 8x\) is \(x < -8\).