Question

When solving the problem 45x−3=16x+6 , your friend does the following: 45x−3=4x+6 5x−3=x+6 4x=9 x=94 Was this correct? (1 point) Responses No, in step 2, the 4 should have been distributed to the current exponents. This would change the equation and yield a different final answer. No, in step 2, the 4 should have been distributed to the current exponents. This would change the equation and yield a different final answer. Yes, this is correct. No error was made. Yes, this is correct. No error was made. No, in step 1 when the 16 changed to 4, it should have been 42 and the 2 distributed to the current exponent. No, in step 1 when the 16 changed to 4, it should have been 4 squared and the 2 distributed to the current exponent. No, the bases of 4 and 16 should have both been changed to a base of 2. No, the bases of 4 and 16 should have both been changed to a base of 2.

Answer 1

Let's analyze the steps your friend took in solving the equation \( 45x - 3 = 16x + 6 \).

1. The original equation is:
\[
45x - 3 = 16x + 6
\]

2. In their first transformation, your friend incorrectly simplified \( 16x \) to \( 4x \):
\[
45x - 3 = 4x + 6
\]
This is the first mistake. The correct transformation should have retained \( 16x \).

3. They then moved to the next step, which is:
\[
5x - 3 = x + 6
\]
This is a follow-up from their previous erroneous step.

4. Continuing, they transitioned to:
\[
4x = 9
\]

5. Finally, they concluded with:
\[
x = \frac{9}{4}
\]

Now, looking at the options for errors:

- Your friend's initial simplification was incorrect when they changed \( 16x \) to \( 4x \). From there, all subsequent steps were based on that initial incorrect premise.

Based on this analysis, the correct response to whether your friend's solution was correct is:

**No, in step 1 when the 16 changed to 4, it should have been left as 16.**