Question

Roy and Sam start solving the equation as follows.

Which student's work is correct so far and what property did he use?

A.
Sam's work is correct so far. He used the addition property of equality.
B.
Roy's work is correct so far. He used the addition property of equality.
C.
Sam's work is correct so far. He used the subtraction property of equality.
D.
Roy's work is correct so far. He used the subtraction property of equality.

Answer 1

The correct option is D.

Explanation:

The given equation is

`-3x+4=5x-6`

According to the addition property of equality
`a=b` and
`a+c=b+c` are equivalent equations.

Use addition property of equality, add 3x on both the sides.

`-3x+4+3x=5x-6+3x`

`4=8x-6`

Therefore Sam's work is incorrect because he make calculation mistake.

According to the subtraction property of equality
`a=b` and
`a-c=b-c` are equivalent equations.

Use subtraction property of equality, subtract 5x from both the sides.

`-3x+4-5x=5x-6-5x`

`-8x+4=-6`

Therefore Roy's work is correct because he used subtraction property.

Option D is correct.