Certainly! Let's solve the equation [tex]\(6(1 + 5x) = 5(1 + 6x)\)[/tex] step-by-step:
1. Distribute the constants on both sides of the equation:
On the left side:
[tex]\[
6(1 + 5x) = 6 \cdot 1 + 6 \cdot 5x = 6 + 30x
\][/tex]
On the right side:
[tex]\[
5(1 + 6x) = 5 \cdot 1 + 5 \cdot 6x = 5 + 30x
\][/tex]
Now, your equation looks like this:
[tex]\[
6 + 30x = 5 + 30x
\][/tex]
2. Move the variable term [tex]\(30x\)[/tex] to both sides to isolate the constants:
Subtract [tex]\(30x\)[/tex] from both sides of the equation:
[tex]\[
6 + 30x - 30x = 5 + 30x - 30x
\][/tex]
Simplifying this, we get:
[tex]\[
6 = 5
\][/tex]
3. Analyze the resulting statement:
The statement [tex]\(6 = 5\)[/tex] is clearly false. This indicates that there is a contradiction without any variable involvement. Therefore, there are no values of [tex]\(x\)[/tex] that can satisfy the original equation.
Hence, the final conclusion is:
[tex]\[
\boxed{The \, equation \, 6(1 + 5x) = 5(1 + 6x) \, has \, no \, solution.}
\][/tex]
