We are given the expression $2^x - 6 + 2^x$, and we want to rewrite it in the form $A \cdot 2^x$.

Step-by-step process:

1. Start by identifying the like terms involving $2^x$: $2^x - 6 + 2^x = 2^x + 2^x - 6$
2. Combine the $2^x$ terms: $2^x + 2^x = 2 \cdot 2^x$ Now the expression becomes: $2 \cdot 2^x - 6$
3. Factor the expression into the desired form: $2^x (2) - 6$

To match the form $A \cdot 2^x$, we can factor out $2^x$: $A = 2$

Thus, the value of $A$ is 2.

Would you like any further explanation?

Related Questions:

1. How would you solve an equation like $2^x - 6 + 2^x = 0$?
2. How do you solve for $x$ when given expressions involving $2^x$?
3. Can you solve equations involving exponents with different bases?
4. What is the process for factoring terms with the same base in exponential expressions?
5. How do logarithms relate to exponential equations like this?

Tip:

Always look for common terms when simplifying expressions, especially in cases with exponents.