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Simplifying 7a + 5a = 4(a + -8) + 12(a + 9) Combine like terms: 7a + 5a = 12a 12a = 4(a + -8) + 12(a + 9) Reorder the terms: 12a = 4(-8 + a) + 12(a + 9) 12a = (-8 * 4 + a * 4) + 12(a + 9) 12a = (-32 + 4a) + 12(a + 9) Reorder the terms: 12a = -32 + 4a + 12(9 + a) 12a = -32 + 4a + (9 * 12 + a * 12) 12a = -32 + 4a + (108 + 12a) Reorder the terms: 12a = -32 + 108 + 4a + 12a Combine like terms: -32 + 108 = 76 12a = 76 + 4a + 12a Combine like terms: 4a + 12a = 16a 12a = 76 + 16a Solving 12a = 76 + 16a Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-16a' to each side of the equation. 12a + -16a = 76 + 16a + -16a Combine like terms: 12a + -16a = -4a -4a = 76 + 16a + -16a Combine like terms: 16a + -16a = 0 -4a = 76 + 0 -4a = 76 Divide each side by '-4'. a = -19 Simplifying a = -19
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