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Simplifying 8[2 + -1[q + 2(q + -3)] + 1] = 3 + -1(8 + -3q) Reorder the terms: 8[2 + -1[q + 2(-3 + q)] + 1] = 3 + -1(8 + -3q) 8[2 + -1[q + (-3 * 2 + q * 2)] + 1] = 3 + -1(8 + -3q) 8[2 + -1[q + (-6 + 2q)] + 1] = 3 + -1(8 + -3q) Reorder the terms: 8[2 + -1[-6 + q + 2q] + 1] = 3 + -1(8 + -3q) Combine like terms: q + 2q = 3q 8[2 + -1[-6 + 3q] + 1] = 3 + -1(8 + -3q) 8[2 + [-6 * -1 + 3q * -1] + 1] = 3 + -1(8 + -3q) 8[2 + [6 + -3q] + 1] = 3 + -1(8 + -3q) Reorder the terms: 8[2 + 6 + 1 + -3q] = 3 + -1(8 + -3q) Combine like terms: 2 + 6 = 8 8[8 + 1 + -3q] = 3 + -1(8 + -3q) Combine like terms: 8 + 1 = 9 8[9 + -3q] = 3 + -1(8 + -3q) [9 * 8 + -3q * 8] = 3 + -1(8 + -3q) [72 + -24q] = 3 + -1(8 + -3q) 72 + -24q = 3 + (8 * -1 + -3q * -1) 72 + -24q = 3 + (-8 + 3q) Combine like terms: 3 + -8 = -5 72 + -24q = -5 + 3q Solving 72 + -24q = -5 + 3q Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-3q' to each side of the equation. 72 + -24q + -3q = -5 + 3q + -3q Combine like terms: -24q + -3q = -27q 72 + -27q = -5 + 3q + -3q Combine like terms: 3q + -3q = 0 72 + -27q = -5 + 0 72 + -27q = -5 Add '-72' to each side of the equation. 72 + -72 + -27q = -5 + -72 Combine like terms: 72 + -72 = 0 0 + -27q = -5 + -72 -27q = -5 + -72 Combine like terms: -5 + -72 = -77 -27q = -77 Divide each side by '-27'. q = 2.851851852 Simplifying q = 2.851851852
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