Question

Alicia is solving the equation 2.3 x minus 1.6 = 8.8 minus 2.9 x. Which equations represent possible ways to begin solving for x? Check all that apply.
2.3 x minus 10.4 = negative 2.9 x
5.2 x minus 1.6 = 8.8
Negative 6.5 x minus 1.6 = negative 2.9 x
2.3 x + 1.3 = 8.8
2.3 x = 10.4 minus 2.9 x

Answer 1

To begin solving the equation \(2.3x - 1.6 = 8.8 - 2.9x\), let's manipulate the equation in different ways to isolate \(x\). Here are the potential steps we can take, and we can check which options correspond to valid manipulations:

1. **Add \(2.9x\) to both sides**:
\(2.3x + 2.9x - 1.6 = 8.8\) \(\Rightarrow\) \(5.2x - 1.6 = 8.8\)

2. **Add \(1.6\) to both sides**:
\(2.3x - 1.6 + 1.6 = 8.8 + 1.6\) \(\Rightarrow\) \(2.3x = 10.4 + 2.9x\)

Now, let's review the options provided:

1. **\(2.3x - 10.4 = -2.9x\)**: This is not a correctly manipulated initial step.

2. **\(5.2x - 1.6 = 8.8\)**: This is a possible way to begin solving. **(Correct)**

3. **\(-6.5x - 1.6 = -2.9x\)**: This is not a valid manipulation of the original equation.

4. **\(2.3x + 1.3 = 8.8\)**: This is not an accurate manipulation of the original equation.

5. **\(2.3x = 10.4 - 2.9x\)**: This represents a valid rearrangement of the equation. **(Correct)**

Thus, the correct options from the choices given are:

- **\(5.2x - 1.6 = 8.8\)**
- **\(2.3x = 10.4 - 2.9x\)**