Answer:
The correct option is D.
Step-by-step explanation:
The given equation is
[tex]-3x+4=5x-6[/tex]
According to the addition property of equality [tex]a=b[/tex] and [tex]a+c=b+c[/tex] are equivalent equations.
Use addition property of equality, add 3x on both the sides.
[tex]-3x+4+3x=5x-6+3x[/tex]
[tex]4=8x-6[/tex]
Therefore Sam's work is incorrect because he make calculation mistake.
According to the subtraction property of equality [tex]a=b[/tex] and [tex]a-c=b-c[/tex] are equivalent equations.
Use subtraction property of equality, subtract 5x from both the sides.
[tex]-3x+4-5x=5x-6-5x[/tex]
[tex]-8x+4=-6[/tex]
Therefore Roy's work is correct because he used subtraction property.
Option D is correct.