Question 1051100
.
-5|3+4k|=-115
~~~~~~~~~~~~~~~~


<pre>
-5|3+4k|=-115  --->

|3 + 4k| = {{{-115/(-5)}}}  --->

|3 + 4k| = 23  --->


a)  3 + 4k = 23  --->  4k = 23 - 3  --->  k = {{{20/4}}} = 5.


b)  3 + 4k = -23  --->  4k = -23 - 3  --->  k = {{{-26/4}}} = -6.5.

<U>Answer</U>.  There are two solutions for k:  k=5  and  k = -6.5.
</pre>

See the figure below:

{{{graph( 330, 330, -10.5, 10.5, -120.5, 10.5,
          (-5)*abs(3+4x), -115
)}}}


Plots y = {{{(-5)*abs(3+4x)}}} (red) and y = -115 (green)


On solving absolute value equations see the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/absolute-value/-Absolute-Value-equations.lesson>Absolute Value equations</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/absolute-value/HOW-TO-solve-equations-containing-Linear-Terms-under-Abs-Value-sign-L-1.lesson>HOW TO solve equations containing Linear Terms under the Absolute Value sign. Lesson 1</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/absolute-value/HOW-TO-solve-equations-containing-Linear-Terms-under-Abs-Value-sign-L-2.lesson>HOW TO solve equations containing Linear Terms under the Absolute Value sign. Lesson 2</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/absolute-value/HOW-TO-solve-equations-containing-Linear-Terms-under-Abs-Value-sign-L-3.lesson>HOW TO solve equations containing Linear Terms under the Absolute Value sign. Lesson 3</A>

in this site.


Also, you have this free of charge online textbook in ALGEBRA-I in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this textbook under the topic "<U>Solving Absolute values equations</U>".