To solve the given expression [tex]\( 6(a + 2b + 3c) \)[/tex] by distributing the coefficient 6 to each term inside the parentheses, follow these steps:
1. Identify the terms inside the parentheses:
[tex]\[
a + 2b + 3c
\][/tex]
2. Distribute the 6 to each term:
[tex]\[
6 \cdot a + 6 \cdot 2b + 6 \cdot 3c
\][/tex]
3. Multiply the constants:
[tex]\[
6 \cdot a = 6a
\][/tex]
[tex]\[
6 \cdot 2b = 12b
\][/tex]
[tex]\[
6 \cdot 3c = 18c
\][/tex]
4. Combine all the terms:
[tex]\[
6a + 12b + 18c
\][/tex]
Therefore, the equivalent expression with the fewest symbols possible is:
[tex]\[
6(a + 2b + 3c) = 6a + 12b + 18c
\][/tex]
