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Simplifying 1 + 11a + 12 + 2a = -3(4 + 12a) + 10(1 + 5a) Reorder the terms: 1 + 12 + 11a + 2a = -3(4 + 12a) + 10(1 + 5a) Combine like terms: 1 + 12 = 13 13 + 11a + 2a = -3(4 + 12a) + 10(1 + 5a) Combine like terms: 11a + 2a = 13a 13 + 13a = -3(4 + 12a) + 10(1 + 5a) 13 + 13a = (4 * -3 + 12a * -3) + 10(1 + 5a) 13 + 13a = (-12 + -36a) + 10(1 + 5a) 13 + 13a = -12 + -36a + (1 * 10 + 5a * 10) 13 + 13a = -12 + -36a + (10 + 50a) Reorder the terms: 13 + 13a = -12 + 10 + -36a + 50a Combine like terms: -12 + 10 = -2 13 + 13a = -2 + -36a + 50a Combine like terms: -36a + 50a = 14a 13 + 13a = -2 + 14a Solving 13 + 13a = -2 + 14a Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-14a' to each side of the equation. 13 + 13a + -14a = -2 + 14a + -14a Combine like terms: 13a + -14a = -1a 13 + -1a = -2 + 14a + -14a Combine like terms: 14a + -14a = 0 13 + -1a = -2 + 0 13 + -1a = -2 Add '-13' to each side of the equation. 13 + -13 + -1a = -2 + -13 Combine like terms: 13 + -13 = 0 0 + -1a = -2 + -13 -1a = -2 + -13 Combine like terms: -2 + -13 = -15 -1a = -15 Divide each side by '-1'. a = 15 Simplifying a = 15
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