Question

Does this equation have infinite solutions, no solution or one solution?
3(4x + 8) = 4(3x + 6)

Answer 1

Let's solve the equation step by step:

The original equation is:

\[
3(4x + 8) = 4(3x + 6)
\]

Expanding both sides:

Left side:
\[
3(4x) + 3(8) = 12x + 24
\]

Right side:
\[
4(3x) + 4(6) = 12x + 24
\]

Now, we can rewrite the equation as:

\[
12x + 24 = 12x + 24
\]

If we subtract \(12x\) from both sides:

\[
24 = 24
\]

This statement is always true. It shows that the original equation holds for any value of \(x\).

Thus, there are **infinite solutions** to the equation.