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Simplifying 1 + -1a + 3a + 7 = -7(1 + -1a) + -5(1 + -1a) Reorder the terms: 1 + 7 + -1a + 3a = -7(1 + -1a) + -5(1 + -1a) Combine like terms: 1 + 7 = 8 8 + -1a + 3a = -7(1 + -1a) + -5(1 + -1a) Combine like terms: -1a + 3a = 2a 8 + 2a = -7(1 + -1a) + -5(1 + -1a) 8 + 2a = (1 * -7 + -1a * -7) + -5(1 + -1a) 8 + 2a = (-7 + 7a) + -5(1 + -1a) 8 + 2a = -7 + 7a + (1 * -5 + -1a * -5) 8 + 2a = -7 + 7a + (-5 + 5a) Reorder the terms: 8 + 2a = -7 + -5 + 7a + 5a Combine like terms: -7 + -5 = -12 8 + 2a = -12 + 7a + 5a Combine like terms: 7a + 5a = 12a 8 + 2a = -12 + 12a Solving 8 + 2a = -12 + 12a Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-12a' to each side of the equation. 8 + 2a + -12a = -12 + 12a + -12a Combine like terms: 2a + -12a = -10a 8 + -10a = -12 + 12a + -12a Combine like terms: 12a + -12a = 0 8 + -10a = -12 + 0 8 + -10a = -12 Add '-8' to each side of the equation. 8 + -8 + -10a = -12 + -8 Combine like terms: 8 + -8 = 0 0 + -10a = -12 + -8 -10a = -12 + -8 Combine like terms: -12 + -8 = -20 -10a = -20 Divide each side by '-10'. a = 2 Simplifying a = 2
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