Math

Question Simplify the given real number equation by identifying the property that justifies the steps.
13x1=(12x+15)+7x13x - 1 = (12x + 15) + 7x 13x1=7x+(12x+15)13x - 1 = 7x + (12x + 15)

Studdy Solution

STEP 1

Assumptions
1. We are dealing with the properties of real numbers.
2. The equation is showing two forms of the same expression.
3. We need to identify which property of real numbers is used to go from the first form to the second form.

STEP 2

Examine the given expressions to understand the change from the first to the second.
The first expression is: 13x1=(12x+15)+7x13x - 1 = (12x + 15) + 7x
The second expression is: 13x1=7x+(12x+15)13x - 1 = 7x + (12x + 15)

STEP 3

Notice that the only change between the two expressions is the order of the terms on the right-hand side of the equation.

STEP 4

Recall the properties of real numbers to identify which property allows for the reordering of terms.

STEP 5

Identify the property as the Commutative Property of Addition, which states that the order in which two numbers are added does not change the sum.
a+b=b+aa + b = b + a

STEP 6

Apply the Commutative Property of Addition to the terms on the right-hand side of the equation.
(12x+15)+7x=7x+(12x+15) (12x + 15) + 7x = 7x + (12x + 15)

STEP 7

Conclude that the Commutative Property of Addition justifies the work shown in the problem.
The property of real numbers that justifies the work shown is the Commutative Property of Addition.

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