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

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Discussion Overview

The discussion revolves around solving the absolute value equation |(2x + 1)|/|(3x + 4)| = 1. Participants explore various methods to approach the solution, including algebraic manipulations and hints related to similar equations.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • Some participants suggest starting by considering the equation 5/x = 1 as a reference for solving the absolute value equation.
  • There is a proposal to multiply both sides of the absolute value equation by |x| to eliminate the denominator.
  • One participant mentions squaring both sides of the equation, leading to a quadratic equation: 0 = 5x^2 + 20x + 15, which simplifies to 0 = x^2 + 4x + 3.
  • The solutions x = -3 and x = -1 are presented as potential solutions to the quadratic equation derived from the original absolute value equation.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the best method to solve the absolute value equation, with multiple approaches being discussed and no clear agreement on the validity of the proposed methods.

Contextual Notes

Some assumptions about the manipulation of absolute values and the implications of squaring both sides may not be fully explored, leaving certain steps unresolved.

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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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