MHB Solve Absolute Value Equation |(2x + 1)|/|(3x + 4)| = 1

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To solve the absolute value equation |(2x + 1)|/|(3x + 4)| = 1, the initial step involves removing the fraction by multiplying both sides by |3x + 4|. Squaring both sides is also suggested as a method to simplify the equation. After manipulation, the resulting quadratic equation is 0 = x^2 + 4x + 3, which factors to find the solutions x = -3 and x = -1. These solutions must be verified within the context of the original absolute value equation. The discussion emphasizes the importance of proper algebraic techniques in solving absolute value equations.
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Solve the absolute value equation.

|(2x + 1)|/|(3x + 4)| = 1
 
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RTCNTC said:
Solve the absolute value equation.

|(2x + 1)|/|(3x + 4)| = 1
Hint: What's the first thing you do to solve the equation [math]\dfrac{5}{x} = 1[/math] ?

-Dan
 
topsquark said:
Hint: What's the first thing you do to solve the equation [math]\dfrac{5}{x} = 1[/math] ?

-Dan

In the equation 5/x = 1, the first thing we do is multiply both sides of the equation by x to remove the fraction on the left side.

Are you saying that I must multiply both sides of the posted question by | x |?
 
RTCNTC said:
In the equation 5/x = 1, the first thing we do is multiply both sides of the equation by x to remove the fraction on the left side.

Are you saying that I must multiply both sides of the posted question by | x |?

Will that allow you to divide out the denominator on the LHS?
 
Someone suggested for me to square both sides.

After doing so, I got

4x^2 + 4x + 1 = 9x^2 + 24x + 16
0 = 5x^2 + 20x + 15
0 = x^2 + 4x + 3

x = -3, -1
 

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