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Simplifying 0.75(2a + -6) + 0.5 = 0.4(3a + 20) Reorder the terms: 0.75(-6 + 2a) + 0.5 = 0.4(3a + 20) (-6 * 0.75 + 2a * 0.75) + 0.5 = 0.4(3a + 20) (-4.5 + 1.5a) + 0.5 = 0.4(3a + 20) Reorder the terms: -4.5 + 0.5 + 1.5a = 0.4(3a + 20) Combine like terms: -4.5 + 0.5 = -4 -4 + 1.5a = 0.4(3a + 20) Reorder the terms: -4 + 1.5a = 0.4(20 + 3a) -4 + 1.5a = (20 * 0.4 + 3a * 0.4) -4 + 1.5a = (8 + 1.2a) Solving -4 + 1.5a = 8 + 1.2a Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1.2a' to each side of the equation. -4 + 1.5a + -1.2a = 8 + 1.2a + -1.2a Combine like terms: 1.5a + -1.2a = 0.3a -4 + 0.3a = 8 + 1.2a + -1.2a Combine like terms: 1.2a + -1.2a = 0.0 -4 + 0.3a = 8 + 0.0 -4 + 0.3a = 8 Add '4' to each side of the equation. -4 + 4 + 0.3a = 8 + 4 Combine like terms: -4 + 4 = 0 0 + 0.3a = 8 + 4 0.3a = 8 + 4 Combine like terms: 8 + 4 = 12 0.3a = 12 Divide each side by '0.3'. a = 40 Simplifying a = 40
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