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Simplifying 3(4a + -5) + -1(3a + 5) = 16 + -1(2a + 3) Reorder the terms: 3(-5 + 4a) + -1(3a + 5) = 16 + -1(2a + 3) (-5 * 3 + 4a * 3) + -1(3a + 5) = 16 + -1(2a + 3) (-15 + 12a) + -1(3a + 5) = 16 + -1(2a + 3) Reorder the terms: -15 + 12a + -1(5 + 3a) = 16 + -1(2a + 3) -15 + 12a + (5 * -1 + 3a * -1) = 16 + -1(2a + 3) -15 + 12a + (-5 + -3a) = 16 + -1(2a + 3) Reorder the terms: -15 + -5 + 12a + -3a = 16 + -1(2a + 3) Combine like terms: -15 + -5 = -20 -20 + 12a + -3a = 16 + -1(2a + 3) Combine like terms: 12a + -3a = 9a -20 + 9a = 16 + -1(2a + 3) Reorder the terms: -20 + 9a = 16 + -1(3 + 2a) -20 + 9a = 16 + (3 * -1 + 2a * -1) -20 + 9a = 16 + (-3 + -2a) Combine like terms: 16 + -3 = 13 -20 + 9a = 13 + -2a Solving -20 + 9a = 13 + -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. -20 + 9a + 2a = 13 + -2a + 2a Combine like terms: 9a + 2a = 11a -20 + 11a = 13 + -2a + 2a Combine like terms: -2a + 2a = 0 -20 + 11a = 13 + 0 -20 + 11a = 13 Add '20' to each side of the equation. -20 + 20 + 11a = 13 + 20 Combine like terms: -20 + 20 = 0 0 + 11a = 13 + 20 11a = 13 + 20 Combine like terms: 13 + 20 = 33 11a = 33 Divide each side by '11'. a = 3 Simplifying a = 3
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