Respuesta :
Let's rewrite the equation as
[tex] |3x+k| = 1-4 = -3 [/tex]
This should be enough to convince you that the equation has no solutions, no matter which value for k you choose. In fact, the left hand side of the equation is an absolute value, which by definition is always positive, or zero in the worst case.
The equality asks for this quantity to equal -3, a negative number.
A non-negative quantity can never equal a stricktly negative quantity, so the equation has no solutions.
You can use the fact that the |x| operation can have the least value as 0.
For any real number value of k, the given equation has no solution.
How to determine for when does an equation gets no solution?
Sometimes is super easy. For example [tex]x - x = 4[/tex]
You know that for any value of x, the equation is not going to be true, so no solution for the given equation.
But sometimes its impossible to find.
And sometimes, it can be found but not that easy as in previous solution.
An equation is said to be having no solution when for any valid value of its variable, the equation is not evaluating true.
The given equation is [tex]|3x-k|+4 = 1[/tex]
We know that
[tex]|x| \geq 0 ; \: \: x \in \mathbb R[/tex]
Thus, we are going to have the left side of the equation always bigger or equal to 4. It is never going to go down than 4, so the equation is not going to be true for any value inside those bars, so it doesn't matter what real number k be, the equation is never going to be true (and this is why, it doesn't matter if x is given or not).
Thus,
For any real number value of k, the given equation has no solution.
Learn more about solutions of equations here:
https://brainly.com/question/11611642
