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Simplifying 5 + -2[3(42 + 7a) + 4(2 + a)] = 6[5(3a + 20) + 2(11 + 5a)] + 5 5 + -2[(42 * 3 + 7a * 3) + 4(2 + a)] = 6[5(3a + 20) + 2(11 + 5a)] + 5 5 + -2[(126 + 21a) + 4(2 + a)] = 6[5(3a + 20) + 2(11 + 5a)] + 5 5 + -2[126 + 21a + (2 * 4 + a * 4)] = 6[5(3a + 20) + 2(11 + 5a)] + 5 5 + -2[126 + 21a + (8 + 4a)] = 6[5(3a + 20) + 2(11 + 5a)] + 5 Reorder the terms: 5 + -2[126 + 8 + 21a + 4a] = 6[5(3a + 20) + 2(11 + 5a)] + 5 Combine like terms: 126 + 8 = 134 5 + -2[134 + 21a + 4a] = 6[5(3a + 20) + 2(11 + 5a)] + 5 Combine like terms: 21a + 4a = 25a 5 + -2[134 + 25a] = 6[5(3a + 20) + 2(11 + 5a)] + 5 5 + [134 * -2 + 25a * -2] = 6[5(3a + 20) + 2(11 + 5a)] + 5 5 + [-268 + -50a] = 6[5(3a + 20) + 2(11 + 5a)] + 5 Combine like terms: 5 + -268 = -263 -263 + -50a = 6[5(3a + 20) + 2(11 + 5a)] + 5 Reorder the terms: -263 + -50a = 6[5(20 + 3a) + 2(11 + 5a)] + 5 -263 + -50a = 6[(20 * 5 + 3a * 5) + 2(11 + 5a)] + 5 -263 + -50a = 6[(100 + 15a) + 2(11 + 5a)] + 5 -263 + -50a = 6[100 + 15a + (11 * 2 + 5a * 2)] + 5 -263 + -50a = 6[100 + 15a + (22 + 10a)] + 5 Reorder the terms: -263 + -50a = 6[100 + 22 + 15a + 10a] + 5 Combine like terms: 100 + 22 = 122 -263 + -50a = 6[122 + 15a + 10a] + 5 Combine like terms: 15a + 10a = 25a -263 + -50a = 6[122 + 25a] + 5 -263 + -50a = [122 * 6 + 25a * 6] + 5 -263 + -50a = [732 + 150a] + 5 Reorder the terms: -263 + -50a = 732 + 5 + 150a Combine like terms: 732 + 5 = 737 -263 + -50a = 737 + 150a Solving -263 + -50a = 737 + 150a Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-150a' to each side of the equation. -263 + -50a + -150a = 737 + 150a + -150a Combine like terms: -50a + -150a = -200a -263 + -200a = 737 + 150a + -150a Combine like terms: 150a + -150a = 0 -263 + -200a = 737 + 0 -263 + -200a = 737 Add '263' to each side of the equation. -263 + 263 + -200a = 737 + 263 Combine like terms: -263 + 263 = 0 0 + -200a = 737 + 263 -200a = 737 + 263 Combine like terms: 737 + 263 = 1000 -200a = 1000 Divide each side by '-200'. a = -5 Simplifying a = -5
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