Question

Which of the following equations has infinite solutions?(1 point)
Responses

−10x+4=10x+3
negative 10 x plus 4 is equal to 10 x plus 3 - no response given

10x+4=10x−4
10 x plus 4 is equal to 10 x minus 4 - incorrect

10x+3=−10x+3
10 x plus 3 is equal to negative 10 x plus 3 - no response given

−10x+4=−10x+4

Answer 1

To determine which of the given equations has infinite solutions, we need to look for an equation that is true for all values of \(x\). This occurs when both sides of the equation are identical for all \(x\).

Let's analyze each equation:

1. **−10x + 4 = 10x + 3**
- Rearranging gives: \(-20x = -1\) or \(x = \frac{1}{20}\) (a single solution).

2. **10x + 4 = 10x − 4**
- Rearranging gives: \(4 = -4\) (which is false, so no solutions).

3. **10x + 3 = −10x + 3**
- Rearranging gives: \(20x = 0\) or \(x = 0\) (a single solution).

4. **−10x + 4 = −10x + 4**
- This is true for all \(x\) (both sides are exactly the same).

The equation with infinite solutions is:

**−10x + 4 = −10x + 4**.