Answer:
[tex]k=-72[/tex]
Step-by-step explanation:
[tex]38=\frac{1}{8} k+47[/tex]
Switching the sides of the equation isn't required, but it helps to reduce confusion.
[tex]\frac{1}{8}k+47=38[/tex]
Since there is a positive 7, we are going to do the opposite operation, which is addition.
[tex]\frac{1}{8}k+47-47=38\\\text\:\:\:\:\:\:-47\:\:\:\:\:\:\:\:\:-47[/tex]
Simplify
+47 - 47 will cancel each other out, so we are left with:
[tex]\frac{1}{8}k=-9[/tex]
Now, multiply 8 to both sides, since the equation gives us 1 divided 8, so the opposite operation of division is multiplication.
[tex]8\cdot \frac{1}{8}k=8\left(-9\right)[/tex]
On the right side, we have the same thing as [tex]\frac{8}{1} \cdot \frac{1}{8}[/tex], so 8 we can cancel the equation on the right side since they are both the same number.
On the left, we have [tex]8\left(-9\right)[/tex], which is -72.
Therefore, [tex]k=-72[/tex].
