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Solve the inequality and graph the solution.

5(w+10)>10
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 \( 5(w+10) > 10 \), we will first simplify it step by step:

  1. Distribute the \( 5 \): \[ 5w + 50 > 10 \]

  2. Subtract \( 50 \) from both sides: \[ 5w > 10 - 50 \] \[ 5w > -40 \]

  3. Divide both sides by \( 5 \): \[ w > -8 \]

The solution to the inequality is \( w > -8 \).

Graphing the Solution

On a number line:

  • You will plot the point \( -8 \).
  • Since the inequality is \( w > -8 \), this point will be represented as an open circle (indicating that \( -8 \) is not included in the solution).
  • The solution extends to the right, indicating all values greater than \( -8 \).

Graph Representation

    <---|---|---|---|---|---|---|---|---|---|---|--->
         -10  -9  -8  -7  -6  -5  -4  -3  -2  -1   0
               (----------------->

In this graph:

  • The point \( -8 \) is an open circle, representing that it is not included in the solution.
  • The line extends to the right from \( -8 \) indicating that all values greater than \( -8 \) are included in the solution.