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Simplifying a + 1 + 7a = 2(4a + -7) + 5(a + -6) Reorder the terms: 1 + a + 7a = 2(4a + -7) + 5(a + -6) Combine like terms: a + 7a = 8a 1 + 8a = 2(4a + -7) + 5(a + -6) Reorder the terms: 1 + 8a = 2(-7 + 4a) + 5(a + -6) 1 + 8a = (-7 * 2 + 4a * 2) + 5(a + -6) 1 + 8a = (-14 + 8a) + 5(a + -6) Reorder the terms: 1 + 8a = -14 + 8a + 5(-6 + a) 1 + 8a = -14 + 8a + (-6 * 5 + a * 5) 1 + 8a = -14 + 8a + (-30 + 5a) Reorder the terms: 1 + 8a = -14 + -30 + 8a + 5a Combine like terms: -14 + -30 = -44 1 + 8a = -44 + 8a + 5a Combine like terms: 8a + 5a = 13a 1 + 8a = -44 + 13a Solving 1 + 8a = -44 + 13a Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-13a' to each side of the equation. 1 + 8a + -13a = -44 + 13a + -13a Combine like terms: 8a + -13a = -5a 1 + -5a = -44 + 13a + -13a Combine like terms: 13a + -13a = 0 1 + -5a = -44 + 0 1 + -5a = -44 Add '-1' to each side of the equation. 1 + -1 + -5a = -44 + -1 Combine like terms: 1 + -1 = 0 0 + -5a = -44 + -1 -5a = -44 + -1 Combine like terms: -44 + -1 = -45 -5a = -45 Divide each side by '-5'. a = 9 Simplifying a = 9
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