Solve for x: -2|x - 3| = -12

Question

unklerhaukus · Answer

-2|x - 3| = -12
      |x-3| =   6
              x= -3 , 6

anonymous · Answer

It's a multi-choice question... It's not that answer...

a) x = -3, x = 9
		
b) x = 3, x = 9
		
c) x = -3, x = 4.5
		
d) No solutions

unklerhaukus · Answer

ops i cant count the answer is x = -3, 9  
 that is a)

anonymous · Answer

The meaning of |x-3| = 6 is the x-values that are exactly 6 units from 3, ie,|dw:1321489063535:dw|So you convert the absolute values equation to$$x-3=\pm6$$or $$x=3\pm6$$which gives$$x=3-6=-3$$or$$x=3+6=9$$

anonymous · Answer

And can you guys help me with these two final questions? :"c

anonymous · Answer

Solve 2|5x - 2| + 4 = 18 for x. Show your work to receive full credit.

unklerhaukus · Answer

2|5x - 2| + 4 = 18
|5x - 2| + 2 = 9
|5x - 2|  = 7

anonymous · Answer

and this one! c: Create an absolute value equation that has two solutions. Explain why this equation has two solutions.

anonymous · Answer

2|5x - 2| + 4 = 18
2|5x - 2| =14             subtract 4
|5x - 2| =7                 divide by 2
5x-2=-7 or 5x-2=7    definition of abs value
5x=-5 or 5x=9           add 2
x=-1 or x=9/5           divide by 5
{-1, 9/5}                    solution set

unklerhaukus · Answer

...follow Mandolino's methods

anonymous · Answer

and this one! c: Create an absolute value equation that has two solutions. Explain why this equation has two solutions.

any abs value equation set equal to a positive number, eg, |x-5|=7
Has two solutions because the interpretation is the x-values that are exactly 7 units from 5.  of course there are two-- one in each direction:|dw:1321489688708:dw|