To solve the equation [tex]\(3(2 - 3x) + 4x = x - 7\)[/tex], the first step is to simplify the expression on the left side. This simplification involves applying a specific mathematical property. Here are the steps explained in detail:
1. Original Equation:
[tex]\[ 3(2 - 3x) + 4x = x - 7 \][/tex]
2. Apply the Distributive Property:
The distributive property states that [tex]\(a(b + c) = ab + ac\)[/tex]. We use this property to multiply 3 by each term inside the parentheses:
[tex]\[ 3 \cdot 2 - 3 \cdot 3x = 6 - 9x \][/tex]
3. Rewrite the Equation:
Now, substituting the distributed values back into the equation, we have:
[tex]\[ 6 - 9x + 4x = x - 7 \][/tex]
4. Combine Like Terms:
Next, we combine like terms on the left side of the equation. The terms [tex]\(-9x\)[/tex] and [tex]\(4x\)[/tex] are like terms:
[tex]\[ 6 - 5x = x - 7 \][/tex]
The correct logical reason for this step is "Distributive Property of Equality" because we used the distributive property to distribute the 3 across the terms inside the parenthesis.
