When solving $2(x+5)=-8$, the property used in the first step is the
A. transitive property
B. substitution property
C. addition property
D. distributive property
Answer (1)
Apply the distributive property to the equation: 2 ( x + 5 ) = 2 x + 10 .
The equation becomes 2 x + 10 = − 8 .
The property used in the first step is the distributive property.
Therefore, the answer is distributive property d i s t r ib u t i v e p ro p er t y .
Explanation
Analyzing the Equation We are given the equation 2 ( x + 5 ) = − 8 and asked to identify the property used in the first step to solve it. Let's analyze the equation and the possible steps we can take.
Applying the Distributive Property The first step in solving the equation 2 ( x + 5 ) = − 8 is to apply the distributive property to eliminate the parentheses. The distributive property states that a ( b + c ) = ab + a c . Applying this to our equation, we get 2 ∗ x + 2 ∗ 5 = − 8 , which simplifies to 2 x + 10 = − 8 .
Identifying the Property Therefore, the property used in the first step is the distributive property.
Examples
The distributive property is a fundamental concept in algebra and is used in many real-world scenarios. For example, if you are buying 3 items that each cost $5 + $2 in tax, you can calculate the total cost as $3 \times (5 + 2) = 3 \times 5 + 3 \times 2 = $15 + $6 = $21. This is an application of the distributive property.
