ANSWER
PART A: D) 6
PART B: C) all real numbers
EXPLANATION
PART A
First we have to apply the distributive property for the -6 in the left term:
[tex]\begin{gathered} -6(x-2)=36-10x \\ -6x+12=36-10x \end{gathered}[/tex]Now we have to put all the terms that contain x on the same side. Add 10x on both sides:
[tex]\begin{gathered} -6x+10x+12=36-10x+10x \\ 4x+12=36 \end{gathered}[/tex]Leave just the term with x on the left term: subtract 12 from both sides:
[tex]\begin{gathered} 4x+12-12=36-12 \\ 4x=24 \end{gathered}[/tex]And finally divide both sides by 4:
[tex]\begin{gathered} \frac{4x}{4}=\frac{24}{4} \\ x=6 \end{gathered}[/tex]PART B
The process for this equation is similar. First we apply the distributive property on the right side:
[tex]\begin{gathered} 64c-16=16\cdot4c-16\cdot1 \\ 64c-16=64c-16 \end{gathered}[/tex]Note that both sides of the equation are the same. This means that any value for c will make this equation true and hence, the solution is all real numbers
