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
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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