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

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SUMMARY

The absolute value equation |(2x + 1)|/|(3x + 4)| = 1 can be solved by first recognizing that it can be transformed into two separate cases: (2x + 1) = (3x + 4) and (2x + 1) = -(3x + 4). By manipulating the equation, the solutions x = -3 and x = -1 are derived after simplifying the resulting quadratic equation 0 = 5x^2 + 20x + 15 to 0 = x^2 + 4x + 3.

PREREQUISITES
  • Understanding of absolute value equations
  • Familiarity with quadratic equations
  • Basic algebraic manipulation skills
  • Knowledge of solving equations involving fractions
NEXT STEPS
  • Study the properties of absolute value functions
  • Learn techniques for solving quadratic equations
  • Explore methods for manipulating rational expressions
  • Investigate the implications of squaring both sides of an equation
USEFUL FOR

Students, educators, and anyone looking to enhance their algebra skills, particularly in solving absolute value and quadratic 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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