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:
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−10x + 4 = 10x + 3
- Rearranging gives: \(-20x = -1\) or \(x = \frac{1}{20}\) (a single solution).
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10x + 4 = 10x − 4
- Rearranging gives: \(4 = -4\) (which is false, so no solutions).
-
10x + 3 = −10x + 3
- Rearranging gives: \(20x = 0\) or \(x = 0\) (a single solution).
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−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.