The equation that has infinitely many solutions is 5(2x + 4) = 10(x + 2).
An equation can have infinitely many solutions when both sides of the equation satisfy the same conditions. The system of an equation has infinitely many solutions when the lines are coincident, and they have the same y-intercept. If the two lines have the same y-intercept and the slope, they are actually in the same exact line. For the given equations it can determine if the equation has infinitely many solutions by simplifying the equation and see if both sides are equal. Hence,
5(2x + 4) = 10x – 12
10x + 20 ≠ 10x - 12
5(2x + 4) = 10(x + 2)
10x + 20 = 10x + 20
5(2x + 4) = 12x
10x + 20 ≠ 12x
5(2x + 10) = 20(x + 1)
10x + 50 ≠ 20x + 20
Hence, 5(2x + 4) = 10(x + 2) has infinitely many solutions.
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