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Simplifying 7(3q + 14) + -31 = 76 + -6(2q + 7) Reorder the terms: 7(14 + 3q) + -31 = 76 + -6(2q + 7) (14 * 7 + 3q * 7) + -31 = 76 + -6(2q + 7) (98 + 21q) + -31 = 76 + -6(2q + 7) Reorder the terms: 98 + -31 + 21q = 76 + -6(2q + 7) Combine like terms: 98 + -31 = 67 67 + 21q = 76 + -6(2q + 7) Reorder the terms: 67 + 21q = 76 + -6(7 + 2q) 67 + 21q = 76 + (7 * -6 + 2q * -6) 67 + 21q = 76 + (-42 + -12q) Combine like terms: 76 + -42 = 34 67 + 21q = 34 + -12q Solving 67 + 21q = 34 + -12q Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '12q' to each side of the equation. 67 + 21q + 12q = 34 + -12q + 12q Combine like terms: 21q + 12q = 33q 67 + 33q = 34 + -12q + 12q Combine like terms: -12q + 12q = 0 67 + 33q = 34 + 0 67 + 33q = 34 Add '-67' to each side of the equation. 67 + -67 + 33q = 34 + -67 Combine like terms: 67 + -67 = 0 0 + 33q = 34 + -67 33q = 34 + -67 Combine like terms: 34 + -67 = -33 33q = -33 Divide each side by '33'. q = -1 Simplifying q = -1
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