Question

Which equation has infinite solutions
-10x + 4 = -10x + 4
-10x + 4 = 10x + 3
10x + 3 = -10x + 3
10x + 4 = 10x - 4

Answer 1

To determine which equations have infinite solutions, we need to analyze each equation to see if they simplify to a true statement (like \(0 = 0\)) or if they yield a specific value for \(x\).

1. **Equation 1**: \(-10x + 4 = -10x + 4\)
- This simplifies to \(0 = 0\). This is always true regardless of the value of \(x\), so it has infinite solutions.

2. **Equation 2**: \(-10x + 4 = 10x + 3\)
- Rearranging gives: \(-10x - 10x = 3 - 4\)
- Simplifies to \(-20x = -1\), so \(x = \frac{1}{20}\). This has a unique solution.

3. **Equation 3**: \(10x + 3 = -10x + 3\)
- Rearranging gives: \(10x + 10x = 3 - 3\)
- Simplifies to \(20x = 0\), so \(x = 0\). This has a unique solution.

4. **Equation 4**: \(10x + 4 = 10x - 4\)
- Rearranging gives: \(10x - 10x = -4 - 4\)
- Simplifies to \(0 = -8\), which is false. This has no solutions.

The only equation that has infinite solutions is **Equation 1**: \(-10x + 4 = -10x + 4\).