Answer:
[tex]c = 5[/tex], explanation for how to get there
Step-by-step explanation:
If we have the equation [tex]4|3c+5| = 16c[/tex], we want to isolate c on one side and find it's value.
Let's first divide both sides by 4.
[tex]4|3c+5|\div4 = 16c\div4\\\\|3c + 5| = 4c[/tex]
Now let's solve for the absolute value. We know that:
[tex]3c + 5 = 4c[/tex]
or
[tex]3c + 5 = -4c[/tex]
Possibility 1:
[tex]3c + 5 = 4c[/tex]
Subtract 3c from both sides:
[tex]5 = c[/tex]
Possibility 2:
[tex]3c + 5 = -4c[/tex]
Add 4c to both sides:
[tex]7c + 5 = 0[/tex]
Subtract 5 from both sides:
[tex]7c = -5[/tex]
Divide both sides by 7:
[tex]c = \frac{-5}{7}[/tex]
Plugging both of these values into the equation, we can see that only 5 works.
Hope this helped!
