We can add or subtract only like quantities. Like terms are terms whose variables are the same. For two or more terms to be called like terms, the variables, including their respective exponents , must be identical. However, the numerical coefficients of these identical variables may be different. Hence, when the sign is dropped, change the sign of each enclosed term.
Equivalent equations are equations whose solution set is the same.
The addition property of equality is traditionally stated two ways with the same result. These are given below. Although the properties as stated in these sections address addition and multiplication, the same properties are appropriate for subtraction and division. This is explained in the notes on pages 91 and 97 of your text.