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Simplifying 4(2q + 1) + -5(3q + 1) = 11q + -1 Reorder the terms: 4(1 + 2q) + -5(3q + 1) = 11q + -1 (1 * 4 + 2q * 4) + -5(3q + 1) = 11q + -1 (4 + 8q) + -5(3q + 1) = 11q + -1 Reorder the terms: 4 + 8q + -5(1 + 3q) = 11q + -1 4 + 8q + (1 * -5 + 3q * -5) = 11q + -1 4 + 8q + (-5 + -15q) = 11q + -1 Reorder the terms: 4 + -5 + 8q + -15q = 11q + -1 Combine like terms: 4 + -5 = -1 -1 + 8q + -15q = 11q + -1 Combine like terms: 8q + -15q = -7q -1 + -7q = 11q + -1 Reorder the terms: -1 + -7q = -1 + 11q Add '1' to each side of the equation. -1 + 1 + -7q = -1 + 1 + 11q Combine like terms: -1 + 1 = 0 0 + -7q = -1 + 1 + 11q -7q = -1 + 1 + 11q Combine like terms: -1 + 1 = 0 -7q = 0 + 11q -7q = 11q Solving -7q = 11q Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-11q' to each side of the equation. -7q + -11q = 11q + -11q Combine like terms: -7q + -11q = -18q -18q = 11q + -11q Combine like terms: 11q + -11q = 0 -18q = 0 Divide each side by '-18'. q = 0 Simplifying q = 0
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