Let's solve the equation step-by-step:
Given the equation:
[tex]\[
\frac{1}{3}(6x + 12) - 2(x - 7) = 19
\][/tex]
1. Distribute the constants inside the parentheses:
- For the term [tex]\(\frac{1}{3}(6x + 12)\)[/tex]:
[tex]\[
\frac{1}{3} \cdot 6x + \frac{1}{3} \cdot 12 = 2x + 4
\][/tex]
- For the term [tex]\(-2(x - 7)\)[/tex]:
[tex]\[
-2 \cdot x + (-2) \cdot (-7) = -2x + 14
\][/tex]
2. Rewrite the equation with the distributed terms:
[tex]\[
2x + 4 - 2x + 14 = 19
\][/tex]
3. Combine like terms:
[tex]\[
2x - 2x + 4 + 14 = 19
\][/tex]
4. Simplify the equation:
[tex]\[
0x + 18 = 19
\][/tex]
5. This simplifies to:
[tex]\[
18 = 19
\][/tex]
As seen, we arrive at a false statement: [tex]\(18 \neq 19\)[/tex]. Therefore, the given equation has no solution. Hence, we conclude that:
[tex]\[
\boxed{\text{There is no solution to the equation.}}
\][/tex]
