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Simplifying 0.5(3a + 1) + 0.75(2a + -1) = 4.25 Reorder the terms: 0.5(1 + 3a) + 0.75(2a + -1) = 4.25 (1 * 0.5 + 3a * 0.5) + 0.75(2a + -1) = 4.25 (0.5 + 1.5a) + 0.75(2a + -1) = 4.25 Reorder the terms: 0.5 + 1.5a + 0.75(-1 + 2a) = 4.25 0.5 + 1.5a + (-1 * 0.75 + 2a * 0.75) = 4.25 0.5 + 1.5a + (-0.75 + 1.5a) = 4.25 Reorder the terms: 0.5 + -0.75 + 1.5a + 1.5a = 4.25 Combine like terms: 0.5 + -0.75 = -0.25 -0.25 + 1.5a + 1.5a = 4.25 Combine like terms: 1.5a + 1.5a = 3a -0.25 + 3a = 4.25 Solving -0.25 + 3a = 4.25 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + 3a = 4.25 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + 3a = 4.25 + 0.25 3a = 4.25 + 0.25 Combine like terms: 4.25 + 0.25 = 4.5 3a = 4.5 Divide each side by '3'. a = 1.5 Simplifying a = 1.5
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