Math

Question Identify the property that justifies the equation: 5(x3)=5x155(x-3)=5x-15. Options: A) multiplication, B) transitive, C) subtraction, D) distributive.

Studdy Solution

STEP 1

Assumptions
1. We need to identify the property of arithmetic that justifies the given mathematical statement.
2. The given statement is 5(x3)=5x155(x-3)=5x-15.

STEP 2

Understand the properties of arithmetic that are listed as options.
A. Multiplication property refers to the ability to multiply numbers together. B. Transitive property refers to the relation between three elements such that if the relation holds between the first and second and between the second and third, it also holds between the first and third. C. Subtraction property would refer to the rules governing the operation of subtraction. D. Distributive property refers to the rule that a number multiplied by the sum of two addends is equal to the sum of the individual products of the number and each addend.

STEP 3

Analyze the given statement to determine which property is being used.
The statement 5(x3)=5x155(x-3)=5x-15 shows a number (5) being multiplied by a binomial (x3)(x-3), and then this multiplication is shown to be equivalent to the number being multiplied by each term of the binomial separately and then subtracting the products.

STEP 4

Match the analysis with the correct property.
Based on the analysis in STEP_3, the property being used is the distributive property, as it involves the distribution of multiplication over subtraction within the binomial.

STEP 5

Select the correct answer.
The correct property that justifies the statement 5(x3)=5x155(x-3)=5x-15 is the distributive property.
The answer is D. distributive.

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