Answer:
D. x = 3.5
Explanation:
The properties of equality describe the relation between two equal quantities. Essentially, if an operation is applied on one side of the equation, then it must be applied on the other side to keep the equation balanced.
Division Property of Equality:
The Division Property of Equality says that we must divide both sides of the equation by the same quantity to keep the equation balanced.
Thus, we can divide both sides by 4:
(4(6x – 9.5) / 4 = (46) / 4
6x – 9.5 = 11.5
Addition Property of Equality:
The Addition Property of Equality says that we must add the same quantity to both sides of the equation to keep the equation balanced.
Thus, we can add 9.5 to both sides:
(6x – 9.5) + 9.5 = (11.5) + 9.5
6x = 21
Division Property of Equality:
We apply this property again and divide both sides by 6 to solve for x:
(6x) / 6 = (21) / 6
x = 3.5
Check validity of answer:
We can check that our answer is correct by plugging in 3.5 for x and seeing if we get 46 on both sides of the equation:
4(6 * 3.5 – 9.5) = 46
4(21 – 9.5) = 46
4(11.5) = 46
46 = 46
Thus, x = 3.5 is the correct answer.