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AnswerThe equation with infinite solutions is Option B4 + 2 (x - 5) = ½ (4x - 12)The key way to know if an equation has infinite solutions is shown in Option BIt is equivalent to an equation that has the same variable terms and the same constant terms on either side of the equal sign.ExplanationThe key way to know if an equation has infinite solutions is whenIt is equivalent to an equation that has the same variable terms and the same constant terms on either side of the equal sign.So, we will check each of the equations to know which one satisfies that condition.2x + 1 = -6x + 22x + 6x = 2 - 18x = 1Divide both sides by 8(8x/8) = (1/8)x = (1/8)This is not the equation with infinite solutions.4 + 2 (x - 5) = ½ (4x - 12)4 + 2x - 10 = 2x - 62x - 6 = 2x - 62x - 2x = 6 - 60 = 0This is the equation with infinite solutions.3x - 5 = (1/5) (5x + 15)3x - 5 = x + 33x - x = 3 + 52x = 8Divide both sides by 2(2x/2) = (8/2)x = 4This is not the equation with infinite solutions.Hope this Helps!!!