Question 971537
<table border = 1>
  <tr>
    <th>Step</th>
    <th>Statement</th>
    <th>Reason/Explanation</th>
  </tr>  
  <tr>
    <td>1.</td>
    <td>-3b-2 > 1</td>
    <td>Start with the given inequality</td>
  </tr>
  <tr>
    <td>2.</td>
    <td>-3b-2<font color="blue">+2</font> > 1<font color="blue">+2</font></td>
    <td>Add 2 to both sides</td>
  </tr>
  <tr>
    <td>3.</td>
    <td>-3b+0 > 3</td>
    <td>Combine like terms (notice how the -2 and +2 add to 0)</td>
  </tr>
  <tr>
    <td>4.</td>
    <td>-3b > 3</td>
    <td>That zero goes away (since x+0 = 0+x = x)</td>
  </tr>
  <tr>
    <td>5.</td>
    <td>-3b<font color="blue">/(-3)</font> < 3<font color="blue">/(-3)</font></td>
    <td>Now divide both sides by -3 to isolate b. See <font color="green">Note</font> below</td>
  </tr>
  <tr>
    <td>6.</td>
    <td>b < -1</td>
    <td>Divide</td>
  </tr>
</table>


<font color="green">Note:</font> when you multiply or divide both sides of an inequality by a negative number, the inequality sign will flip.


So the final answer is <font color="red">b < -1</font>


In interval notation, the answer is *[Tex \LARGE (-\infty, -1)]