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Simplifying 7 + -1[4 + 2(a + -3)] = 11(a + 2) Reorder the terms: 7 + -1[4 + 2(-3 + a)] = 11(a + 2) 7 + -1[4 + (-3 * 2 + a * 2)] = 11(a + 2) 7 + -1[4 + (-6 + 2a)] = 11(a + 2) Combine like terms: 4 + -6 = -2 7 + -1[-2 + 2a] = 11(a + 2) 7 + [-2 * -1 + 2a * -1] = 11(a + 2) 7 + [2 + -2a] = 11(a + 2) Combine like terms: 7 + 2 = 9 9 + -2a = 11(a + 2) Reorder the terms: 9 + -2a = 11(2 + a) 9 + -2a = (2 * 11 + a * 11) 9 + -2a = (22 + 11a) Solving 9 + -2a = 22 + 11a Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-11a' to each side of the equation. 9 + -2a + -11a = 22 + 11a + -11a Combine like terms: -2a + -11a = -13a 9 + -13a = 22 + 11a + -11a Combine like terms: 11a + -11a = 0 9 + -13a = 22 + 0 9 + -13a = 22 Add '-9' to each side of the equation. 9 + -9 + -13a = 22 + -9 Combine like terms: 9 + -9 = 0 0 + -13a = 22 + -9 -13a = 22 + -9 Combine like terms: 22 + -9 = 13 -13a = 13 Divide each side by '-13'. a = -1 Simplifying a = -1
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