Question

15. Maggie said that she could add 8 to both sides of the equation would still be equal. Do you agree? Explain

Answer 1

Yes. Yes I do.

If you think of an equation as a balance, where both sides have equal weight, then adding the same amount to both sides or taking away the same amount from both sides will still maintain that balanced weight.

We call this the addition property of equality:

If a = b, then a+c = b+c for any expression c.

Answer 2

It depends on the equation in question. If Maggie is referring to an equation in the form of x = y, then adding 8 to both sides would still result in the same value of x and y being equal. For example, if the equation is 2x - 5 = 7, then adding 8 to both sides would result in 2x - 5 + 8 = 7 + 8, which simplifies to 2x + 3 = 15. In this case, adding 8 to both sides would not maintain equality.

However, if the equation is in the form of an inequality such as x < y or x > y, adding the same value to both sides may not maintain the inequality. For example, if the inequality is 2x - 5 < 7, then adding 8 to both sides would result in 2x - 5 + 8 < 7 + 8, which simplifies to 2x + 3 < 15. In this case, adding 8 to both sides would still maintain the inequality.

Therefore, whether or not adding 8 to both sides of an equation would still result in equality depends on the equation in question and the mathematical operation being performed.