Question

REASONING IN ALGEBRA AND GEOMETRY Fill in the reason that justifies each step

Answer 1

9514 1404 393

Answer:

  1a. multiplication property of equality

  1b. distributive property

  1c. subtraction property of equality

  1d. division property of equality

  2a. distributive property

  2b. addition property of equality

  2c. division property of equality

Step-by-step explanation:

The properties that let you do the same thing to both sides of an equation are the properties of equality. These are usually given an additional qualifier according to the operation being performed: addition property ..., subtraction property ..., multiplication property ..., division property .... The property that lets you add or eliminate parentheses is the distributive property (of multiplication over addition).

To answer these questions, you need to compare each line to the previous to see what operation was performed. It will generally be use of one of the properties described above, or "simplification," in which like terms are combined.

1a. both sides are multiplied by 3: multiplication property of equality

1b. parentheses are eliminated: distributive property

1c. 18 is subtracted from both sides: subtraction property of equality

1d. both sides are divided by 2: division property of equality

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2a. parentheses are eliminated: distributive property

2b. 24 is added to both sides: addition property of equality

2c. both sides are divided by 2: division property of equality