To solve the equation [tex]\(2(x + 6) = 3(x - 4) + 5\)[/tex], we need to follow systematic algebraic steps. A reasonable first step to simplify this equation is to distribute the constants 2 and 3 to their respective expressions within the parentheses.
Here is a detailed step-by-step explanation:
1. Distribute 2 to [tex]\((x + 6)\)[/tex]:
[tex]\[
2(x + 6) = 2 \cdot x + 2 \cdot 6 = 2x + 12
\][/tex]
2. Distribute 3 to [tex]\((x - 4)\)[/tex]:
[tex]\[
3(x - 4) = 3 \cdot x - 3 \cdot 4 = 3x - 12
\][/tex]
By distributing these constants, we rewrite the original equation [tex]\(2(x + 6) = 3(x - 4) + 5\)[/tex] as:
[tex]\[
2x + 12 = 3x - 12 + 5
\][/tex]
Hence, the reasonable first step in solving the equation is:
Distribute 2 to [tex]\((x + 6)\)[/tex] and 3 to [tex]\((x - 4)\)[/tex].
