SOLUTION: How do I begin to solve this equation (absolute value bar)2x+1/3x+4(absolute value bar) = 1

Question 488937: How do I begin to solve this equation (absolute value bar)2x+1/3x+4(absolute value bar) = 1
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
How do I begin to solve this equation (absolute value bar)2x+1/3x+4(absolute value bar) = 1
------------------------
|(2x+1)/(3x+4)| = 1
----
Draw a number line.
Plot x = -1/2 and x = -4//3 on the line
----
Determine the sign of the fraction in each of the three line intervals.
------
If x < -4/3 the fraction is -/- = positive
So (2x+1)/(3x+4) = 1
2x+1 = 3x+4
x = -3
----
If -4/3 < x < -1/2, the fraction is -/+ = negative
So (2x+1)/(3x+4) = -1
2x+1 = -3x-4
5x = -5
x = -1
-------------
If x > -1/2 the fraction is +/+ = positive
You get x = -3 as you did above.
====================================
Cheers,
Stan H.
RELATED QUESTIONS
2 (absolute value bar) 3x-1 (end of absolute vale bar) +5=33 thank... (answered by stanbon)

Evaluate the expression 4-||14|-11| Each vertical bar or "|" = Absolute value. The 14... (answered by jim_thompson5910)

How do you solve this equation? absolute value... (answered by stanbon)

How do I solve: The absolute value of n-6 = the absolute value of... (answered by bucky)

I do not understand how exactly to solve this equation. |x-1|=|3x+2| those are absolute... (answered by stanbon)

Solve and show three forms of the solution: absolute value bar x+3 absolute value bar <_... (answered by edjones)

how do you do this problem about absolute value?:... (answered by Edwin McCravy)

can you please show me how to solve this absolute value equation and inequality?... (answered by stanbon)

|7-1/2x|=-3 how do you solve this absolute... (answered by Cintchr)