Understanding Modulus Equations: Solving for x

[chwala]

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?

 

[fresh_42]

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.

 

[Mark44]

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.

 

[chwala]

there...i just confirmed with problem owner, it was a typo on textbook part. No solution exists. cheers

 

[chwala]

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...

 

[haruspex]

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 $±(2x+3)-x=1$.

 

[chwala]

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...

 

[haruspex]

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.

 

[chwala]

Sure, but you seemed not to understand why readers were confused by your saying you got those values for x.

Ok boss, thanks noted...