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Simplifying 3(a + 5) + -6(2a + -4) = 2(a + 3) Reorder the terms: 3(5 + a) + -6(2a + -4) = 2(a + 3) (5 * 3 + a * 3) + -6(2a + -4) = 2(a + 3) (15 + 3a) + -6(2a + -4) = 2(a + 3) Reorder the terms: 15 + 3a + -6(-4 + 2a) = 2(a + 3) 15 + 3a + (-4 * -6 + 2a * -6) = 2(a + 3) 15 + 3a + (24 + -12a) = 2(a + 3) Reorder the terms: 15 + 24 + 3a + -12a = 2(a + 3) Combine like terms: 15 + 24 = 39 39 + 3a + -12a = 2(a + 3) Combine like terms: 3a + -12a = -9a 39 + -9a = 2(a + 3) Reorder the terms: 39 + -9a = 2(3 + a) 39 + -9a = (3 * 2 + a * 2) 39 + -9a = (6 + 2a) Solving 39 + -9a = 6 + 2a Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2a' to each side of the equation. 39 + -9a + -2a = 6 + 2a + -2a Combine like terms: -9a + -2a = -11a 39 + -11a = 6 + 2a + -2a Combine like terms: 2a + -2a = 0 39 + -11a = 6 + 0 39 + -11a = 6 Add '-39' to each side of the equation. 39 + -39 + -11a = 6 + -39 Combine like terms: 39 + -39 = 0 0 + -11a = 6 + -39 -11a = 6 + -39 Combine like terms: 6 + -39 = -33 -11a = -33 Divide each side by '-11'. a = 3 Simplifying a = 3
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