Understanding Modulus Equations: Solving for x

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In summary, the conversation discusses the equation ##|2x+3|-x=1## and the process of solving modulus equations. The speaker initially finds the solutions ##x=-2## and ##x=\frac{-4}{3}##, but realizes that they do not satisfy the given equation. They suggest drawing graphs to see if the two equations intersect, and the conversation ends with the clarification that the speaker did not actually "get" those values for x, but rather found them as candidates for solutions.
  • #1
chwala
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Homework Statement
##|2x+3|-x=1##
Relevant Equations
modulus
##|2x+3|-x=1##
i am getting ##x=-2## and ##x=\frac {-4}{3}## of which none satisfies the original equation, therefore we do not have a solution, right?
 
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  • #2
What do you mean by getting? If there are no solutions, how can you get values for ##x?## You could draw the graph for ##y=|2x+3|## and the graph for ##y=1+x## and see if they intersect or not.
 
  • #3
chwala said:
Homework Statement:: ##|2x+3|-x=1##
Relevant Equations:: modulus

##|2x+3|-x=1##
i am getting ##x=-2## and ##x=\frac {-4}{3}## of which none satisfies the original equation, therefore we do not have a solution, right?
The equation is equivalent to ##|2x + 3| = x + 1##
Because of the absolute value on the left, it must be true that ##x + 1 \ge 0##, or ##x \ge -1##. Neither of the solutions you found satisfies this additional requirement, so there is no solution.
 
  • #4
1611367692626.png

there...i just confirmed with problem owner, it was a typo on textbook part. No solution exists. cheers
 
  • #5
fresh_42 said:
What do you mean by getting? If there are no solutions, how can you get values for ##x?## You could draw the graph for ##y=|2x+3|## and the graph for ##y=1+x## and see if they intersect or not.

when we solve modulus equations, we first try getting values for ##x## right? then proceed on checking if they satisfy the equation...
 
  • #6
chwala said:
when we solve modulus equations, we first try getting values for ##x## right?
No, but you can get candidate values by ignoring some constraints (which should be specified) and check which resulting solutions satisfy them.
In the present case, you relaxed the given condition ##|2x+3|-x=1## to be ##±(2x+3)-x=1##.
 
  • #7
haruspex said:
No, but you can get candidate values by ignoring some constraints (which should be specified) and check which resulting solutions satisfy them.
In the present case, you relaxed the given condition ##|2x+3|-x=1## to be ##±(2x+3)-x=1##.
Either case, by considering those constraints, you will end up with the values that I found...
 
  • #8
chwala said:
Either case, by considering those constraints, you will end up with the values that I found...
Sure, but you seemed not to understand why readers were confused by your saying you got those values for x.
 
  • #9
haruspex said:
Sure, but you seemed not to understand why readers were confused by your saying you got those values for x.
Ok boss, thanks noted...
 

Related to Understanding Modulus Equations: Solving for x

1. What is a modulus equation?

A modulus equation is an equation that involves the modulus operator, denoted by the symbol "| |". The modulus operator calculates the remainder when one number is divided by another. For example, in the equation 10 | 3, the result would be 1, since 10 divided by 3 has a remainder of 1.

2. How do you solve a modulus equation?

To solve a modulus equation, you must first isolate the modulus expression on one side of the equation. Then, you can use the definition of the modulus operator to rewrite the equation without the modulus symbol. Finally, solve the resulting equation as you would any other algebraic equation.

3. Can a modulus equation have more than one solution?

Yes, a modulus equation can have more than one solution. This is because the modulus operator only gives the remainder of a division, not the actual quotient. For example, in the equation 10 | x = 2, both x = 8 and x = 12 would be valid solutions.

4. Are there any special cases when solving a modulus equation?

Yes, there are two special cases to consider when solving a modulus equation. The first is when the modulus expression is negative, in which case you must take the absolute value of the expression. The second is when the modulus expression is zero, in which case the solution will always be zero.

5. Can a modulus equation have no solution?

Yes, a modulus equation can have no solution. This can occur when the modulus expression is greater than the number on the other side of the equation, or when the modulus expression and the number on the other side have no common factors. In these cases, the equation has no solution.

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