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Simplifying 3(3a + 4) + -9(a + 5) = a + 8(a + -3) Reorder the terms: 3(4 + 3a) + -9(a + 5) = a + 8(a + -3) (4 * 3 + 3a * 3) + -9(a + 5) = a + 8(a + -3) (12 + 9a) + -9(a + 5) = a + 8(a + -3) Reorder the terms: 12 + 9a + -9(5 + a) = a + 8(a + -3) 12 + 9a + (5 * -9 + a * -9) = a + 8(a + -3) 12 + 9a + (-45 + -9a) = a + 8(a + -3) Reorder the terms: 12 + -45 + 9a + -9a = a + 8(a + -3) Combine like terms: 12 + -45 = -33 -33 + 9a + -9a = a + 8(a + -3) Combine like terms: 9a + -9a = 0 -33 + 0 = a + 8(a + -3) -33 = a + 8(a + -3) Reorder the terms: -33 = a + 8(-3 + a) -33 = a + (-3 * 8 + a * 8) -33 = a + (-24 + 8a) Reorder the terms: -33 = -24 + a + 8a Combine like terms: a + 8a = 9a -33 = -24 + 9a Solving -33 = -24 + 9a Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-9a' to each side of the equation. -33 + -9a = -24 + 9a + -9a Combine like terms: 9a + -9a = 0 -33 + -9a = -24 + 0 -33 + -9a = -24 Add '33' to each side of the equation. -33 + 33 + -9a = -24 + 33 Combine like terms: -33 + 33 = 0 0 + -9a = -24 + 33 -9a = -24 + 33 Combine like terms: -24 + 33 = 9 -9a = 9 Divide each side by '-9'. a = -1 Simplifying a = -1
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