SOLUTION: How do you solve this type of absolute value equation? It has a number outside the absolute value symbol that would indicate the distributive property, but it isn't matching the a

Algebra ->  Graphs -> SOLUTION: How do you solve this type of absolute value equation? It has a number outside the absolute value symbol that would indicate the distributive property, but it isn't matching the a      Log On


   

Question 241600: How do you solve this type of absolute value equation? It has a number outside the absolute value symbol that would indicate the distributive property, but it isn't matching the answers in the back when I tried that. Here is an example:
3/5 |3x+2| +5 = y
Would you try the 2 solutions, one positive and one negative? But I can't see how to do that when you don't know what x is.
Thanks!
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The way I approach it is to disassemble it, then put it back together
%283%2F5%29%2Aabs%283x%2B2%29+%2B5+=+y
I'll disregard the 5 and the 3%2F5 for now
abs%283x%2B2%29+=+y
y can never be negative
When x+=+-%282%2F3%29, y+=+0
I'll plot it
+graph%28+400%2C+400%2C+-4%2C+4%2C+-4%2C+4%2C+abs%283x%2B2%29%29+
Now I'll factor in the 3%2F5, and plot that
+graph%28+400%2C+400%2C+-4%2C+4%2C+-4%2C+4%2C++%283%2F5%29%2Aabs%283x%2B2%29%29+
The plot is spread out, since y is now less for every x
Now I'll add 5 to the last plot
+graph%28+400%2C+400%2C+-4%2C+4%2C+-2%2C+8%2C+%283%2F5%29%2Aabs%283x%2B2+%29+%2B+5%29+
Since there are 2 variables, the solution is the plot
Do you want inequalities? You can get those from the plot, too