distributive propertyaddition (subtraction) property of equalityadditive identity element (properties of real numbers)division property of equalitymultiplicative identity element (properties of real numbers)
Step-by-step explanation:
A lot of math is about identifying and matching patterns. Often, the patterns have an associated vocabulary. It helps to learn the patterns and the associated words.
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Pattern: a(b +c) ⇔ ab +ac . . . description: distributive property
Pattern: a = b ⇒ a +c = b +c . . . description: addition property of equality
Pattern: a = b ⇒ a/c = b/c . . . description: division property of equality
Patterns: a -a = 0; a + 0 = a . . . description: properties of the additive inverse and the additive identity element
Patterns: a×(1/a) = 1; a×1 = a . . . description: properties of the multiplicative inverse and the multiplicative identity element
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When parentheses come or go, the distributive property is usually involved. In the second line, you need to recognize that -2(3y) = -6y and that -2(-7) = +14. The result on the left is from applying the distributive property to remove parentheses.
The third line differs from the second line in that -14 shows up on both sides of the equal sign. This is a clue that the addition (or subtraction) property of equality is involved.
The fourth line differs from the third in that +14-14 disappeared from the left side, and -4-14 was replaced with -18 on the right side. The sum of a number and its opposite is zero, a property of the additive inverse. The fact that -4-14 = -18 is a property of real numbers. (You have to decide the best drop-down choice for that line.)
The fifth line shows both sides of the equation divided by -6. The multiplication (division) property of equality lets you do that.
The last line shows a simplification of the previous one. Again, the properties of real numbers and of the multiplicative inverse are involved. (You have to decide the best drop-down choice for that line.)
