text: # How do you solve |10x + 2| - 18 = -12?
  
  Mar 7, 2016
  
  This is an absolute value equation. As a result, we must consider two scenarios: that the absolute value is positive or negative.
  
  #### Explanation:
  
  First, before I solve the equation, let me prove the point I made above to further your understanding.
  
  Let's look at an extremely simple equation involving absolute value.
  
  $| x | = 2$
  
  An absolute value, by definition, means the distance on the number line between 0 and the number. This distance doesn't take into account direction and therefore always is positive.
  
  So, we must consider in the above equation the following:
  
  x = 2 or -x = 2
  
  x = 2 or x = -2
  
  Checking these solutions back in the equation, you'll notice both will work, since $| - 2 | = 2$
  
  We must first isolate the absolute value:
  
  $| 10 x + 2 | = 6$
  
  $10 x + 2 = 6 \mathmr{and} - \left(10 x + 2\right) = 6$
  
  $10 x = 4 \mathmr{and} - 10 x - 2 = 6$
  
  $x = \frac{2}{5} \mathmr{and} - \frac{4}{5}$
  
  Hopefully this helps, and happy voting tomorrow!