What properties are expressed in these equations?

a=b
a + [c + (-c)] = b + [c + (-c)]

Also, would the property expressed in -a=-b be the substitution property of equality?

In both equations, \(a = b\) and \(a + [c + (-c)] = b + [c + (-c)]\), the property being expressed is the addition property of equality.

The addition property of equality states that if you add the same quantity to both sides of an equation, then the resulting equation is still true. In both equations, both sides are being altered by the addition of the expression \([c + (-c)]\). By using this property, we can simplify the equation by canceling out the expression \([c + (-c)]\):

\[a + [c + (-c)] = b + [c + (-c)] \]
\[a + 0 = b + 0 \]
\[a = b \]

So, the property being expressed is the addition property of equality as it is used to simplify the equation.

Regarding the equation \(-a = -b\), the property being expressed is actually the additive inverse property. The additive inverse property states that the sum of a number and its additive inverse is always zero.

In this equation, both sides are being negated, resulting in the equation \(-a = -b\). Here, the additive inverse property is being used because the negation of each side is equivalent to multiplying both sides by -1:

\(-1 \cdot a = -1 \cdot b \)

So, the property being expressed in the equation \(-a = -b\) is the additive inverse property, not the substitution property of equality.