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Simplifying 0.4(2a + 0.5) = 3[0.2a + (-2)] + -4 Reorder the terms: 0.4(0.5 + 2a) = 3[0.2a + (-2)] + -4 (0.5 * 0.4 + 2a * 0.4) = 3[0.2a + (-2)] + -4 (0.2 + 0.8a) = 3[0.2a + (-2)] + -4 0.2 + 0.8a = 3[0.2a + -2] + -4 Reorder the terms: 0.2 + 0.8a = 3[-2 + 0.2a] + -4 0.2 + 0.8a = [-2 * 3 + 0.2a * 3] + -4 0.2 + 0.8a = [-6 + 0.6a] + -4 Reorder the terms: 0.2 + 0.8a = -6 + -4 + 0.6a Combine like terms: -6 + -4 = -10 0.2 + 0.8a = -10 + 0.6a Solving 0.2 + 0.8a = -10 + 0.6a Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.6a' to each side of the equation. 0.2 + 0.8a + -0.6a = -10 + 0.6a + -0.6a Combine like terms: 0.8a + -0.6a = 0.2a 0.2 + 0.2a = -10 + 0.6a + -0.6a Combine like terms: 0.6a + -0.6a = 0.0 0.2 + 0.2a = -10 + 0.0 0.2 + 0.2a = -10 Add '-0.2' to each side of the equation. 0.2 + -0.2 + 0.2a = -10 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + 0.2a = -10 + -0.2 0.2a = -10 + -0.2 Combine like terms: -10 + -0.2 = -10.2 0.2a = -10.2 Divide each side by '0.2'. a = -51 Simplifying a = -51
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