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Solve the inequality and graph the solution.

w+2
2
>
–
1
Plot the endpoints. Select an endpoint to change it from closed to open. Select the middle of the segment, ray, or line to delete it.

1 answer

To solve the inequality:

\[ \frac{w + 2}{2} > -1 \]

we first eliminate the fraction by multiplying both sides by 2 (since 2 is positive, the direction of the inequality remains the same):

\[ w + 2 > -2 \]

Next, we isolate \(w\) by subtracting 2 from both sides:

\[ w > -4 \]

Graphing the Solution:

  1. The endpoint of the inequality is \(w = -4\).
  2. Since the inequality is strict (greater than, not greater than or equal to), we will use an open circle at \(-4\).
  3. The solution includes all values to the right of \(-4\).

Graph Representation:

  • Draw a number line.
  • Place an open circle at \(-4\) to indicate that \(-4\) is not included in the solution.
  • Shade the area to the right of \(-4\) to indicate that all values greater than \(-4\) are part of the solution.

\[ \text{Number Line Representation:} \]

<---|----|----|----|----|----|----|----|---->
   -5   -4   -3   -2   -1    0    1    2
          (-------------------------->

Here, the parentheses \( ( \) indicates that the endpoint \(-4\) is not included in the solution set. The shaded line indicates all numbers greater than \(-4\).