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

In summary, to solve the absolute value equation |(2x + 1)|/|(3x + 4)| = 1, you first multiply both sides by the denominator on the left side to remove the fraction. Then, you can solve the resulting quadratic equation to find the solutions, which in this case are x = -3 and x = -1.
  • #1
mathdad
1,283
1
Solve the absolute value equation.

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

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

-Dan
 
  • #3
topsquark said:
Hint: What's the first thing you do to solve the equation \(\displaystyle \dfrac{5}{x} = 1\) ?

-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 |?
 
  • #4
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?
 
  • #5
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
 

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

What is an absolute value equation?

An absolute value equation is an equation that contains an absolute value expression. In mathematics, the absolute value of a number is its distance from zero on a number line. Absolute value equations often involve finding the value of a variable that makes the equation true.

How do you solve an absolute value equation?

To solve an absolute value equation, you need to isolate the absolute value expression and then solve for the variable. This can be done by setting up two equations, one with the expression inside the absolute value bars and one with the negative of that expression. Then, solve for the variable in each equation and check the solutions by plugging them back into the original equation.

What is the absolute value of a negative number?

The absolute value of a negative number is the positive version of that number. For example, the absolute value of -5 is 5. This is because the absolute value represents the distance from zero, so a negative number's distance from zero is its positive counterpart.

What is the difference between absolute value and magnitude?

Absolute value and magnitude are often used interchangeably, but they have slightly different meanings. Absolute value refers to the distance from zero on a number line, while magnitude refers to the size or extent of a quantity. In other words, absolute value is a specific mathematical concept, while magnitude is a more general term.

How do you check your solution to an absolute value equation?

To check your solution to an absolute value equation, simply plug the solution back into the original equation and see if it makes the equation true. If it does, then it is a valid solution. If not, then you may have made an error in your calculations and should try again.

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