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Simplifying 12q + -6(q + 1) = 4(2q + -1) + -3 Reorder the terms: 12q + -6(1 + q) = 4(2q + -1) + -3 12q + (1 * -6 + q * -6) = 4(2q + -1) + -3 12q + (-6 + -6q) = 4(2q + -1) + -3 Reorder the terms: -6 + 12q + -6q = 4(2q + -1) + -3 Combine like terms: 12q + -6q = 6q -6 + 6q = 4(2q + -1) + -3 Reorder the terms: -6 + 6q = 4(-1 + 2q) + -3 -6 + 6q = (-1 * 4 + 2q * 4) + -3 -6 + 6q = (-4 + 8q) + -3 Reorder the terms: -6 + 6q = -4 + -3 + 8q Combine like terms: -4 + -3 = -7 -6 + 6q = -7 + 8q Solving -6 + 6q = -7 + 8q Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-8q' to each side of the equation. -6 + 6q + -8q = -7 + 8q + -8q Combine like terms: 6q + -8q = -2q -6 + -2q = -7 + 8q + -8q Combine like terms: 8q + -8q = 0 -6 + -2q = -7 + 0 -6 + -2q = -7 Add '6' to each side of the equation. -6 + 6 + -2q = -7 + 6 Combine like terms: -6 + 6 = 0 0 + -2q = -7 + 6 -2q = -7 + 6 Combine like terms: -7 + 6 = -1 -2q = -1 Divide each side by '-2'. q = 0.5 Simplifying q = 0.5
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