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Simplifying 15(2a + 1) = 5(0.5a + 0.3) + 0.1 Reorder the terms: 15(1 + 2a) = 5(0.5a + 0.3) + 0.1 (1 * 15 + 2a * 15) = 5(0.5a + 0.3) + 0.1 (15 + 30a) = 5(0.5a + 0.3) + 0.1 Reorder the terms: 15 + 30a = 5(0.3 + 0.5a) + 0.1 15 + 30a = (0.3 * 5 + 0.5a * 5) + 0.1 15 + 30a = (1.5 + 2.5a) + 0.1 Reorder the terms: 15 + 30a = 1.5 + 0.1 + 2.5a Combine like terms: 1.5 + 0.1 = 1.6 15 + 30a = 1.6 + 2.5a Solving 15 + 30a = 1.6 + 2.5a Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2.5a' to each side of the equation. 15 + 30a + -2.5a = 1.6 + 2.5a + -2.5a Combine like terms: 30a + -2.5a = 27.5a 15 + 27.5a = 1.6 + 2.5a + -2.5a Combine like terms: 2.5a + -2.5a = 0.0 15 + 27.5a = 1.6 + 0.0 15 + 27.5a = 1.6 Add '-15' to each side of the equation. 15 + -15 + 27.5a = 1.6 + -15 Combine like terms: 15 + -15 = 0 0 + 27.5a = 1.6 + -15 27.5a = 1.6 + -15 Combine like terms: 1.6 + -15 = -13.4 27.5a = -13.4 Divide each side by '27.5'. a = -0.4872727273 Simplifying a = -0.4872727273
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