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Simplifying 2[0.5q + 1] = -3[2q + -1] + 4[2q + 1] Reorder the terms: 2[1 + 0.5q] = -3[2q + -1] + 4[2q + 1] [1 * 2 + 0.5q * 2] = -3[2q + -1] + 4[2q + 1] [2 + 1q] = -3[2q + -1] + 4[2q + 1] Reorder the terms: 2 + 1q = -3[-1 + 2q] + 4[2q + 1] 2 + 1q = [-1 * -3 + 2q * -3] + 4[2q + 1] 2 + 1q = [3 + -6q] + 4[2q + 1] Reorder the terms: 2 + 1q = 3 + -6q + 4[1 + 2q] 2 + 1q = 3 + -6q + [1 * 4 + 2q * 4] 2 + 1q = 3 + -6q + [4 + 8q] Reorder the terms: 2 + 1q = 3 + 4 + -6q + 8q Combine like terms: 3 + 4 = 7 2 + 1q = 7 + -6q + 8q Combine like terms: -6q + 8q = 2q 2 + 1q = 7 + 2q Solving 2 + 1q = 7 + 2q Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-2q' to each side of the equation. 2 + 1q + -2q = 7 + 2q + -2q Combine like terms: 1q + -2q = -1q 2 + -1q = 7 + 2q + -2q Combine like terms: 2q + -2q = 0 2 + -1q = 7 + 0 2 + -1q = 7 Add '-2' to each side of the equation. 2 + -2 + -1q = 7 + -2 Combine like terms: 2 + -2 = 0 0 + -1q = 7 + -2 -1q = 7 + -2 Combine like terms: 7 + -2 = 5 -1q = 5 Divide each side by '-1'. q = -5 Simplifying q = -5
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