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Simplifying 2(0.5q + 1) = -3(2q + -1) + 4(2a + 1) Reorder the terms: 2(1 + 0.5q) = -3(2q + -1) + 4(2a + 1) (1 * 2 + 0.5q * 2) = -3(2q + -1) + 4(2a + 1) (2 + 1q) = -3(2q + -1) + 4(2a + 1) Reorder the terms: 2 + 1q = -3(-1 + 2q) + 4(2a + 1) 2 + 1q = (-1 * -3 + 2q * -3) + 4(2a + 1) 2 + 1q = (3 + -6q) + 4(2a + 1) Reorder the terms: 2 + 1q = 3 + -6q + 4(1 + 2a) 2 + 1q = 3 + -6q + (1 * 4 + 2a * 4) 2 + 1q = 3 + -6q + (4 + 8a) Reorder the terms: 2 + 1q = 3 + 4 + 8a + -6q Combine like terms: 3 + 4 = 7 2 + 1q = 7 + 8a + -6q Solving 2 + 1q = 7 + 8a + -6q Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '6q' to each side of the equation. 2 + 1q + 6q = 7 + 8a + -6q + 6q Combine like terms: 1q + 6q = 7q 2 + 7q = 7 + 8a + -6q + 6q Combine like terms: -6q + 6q = 0 2 + 7q = 7 + 8a + 0 2 + 7q = 7 + 8a Add '-2' to each side of the equation. 2 + -2 + 7q = 7 + -2 + 8a Combine like terms: 2 + -2 = 0 0 + 7q = 7 + -2 + 8a 7q = 7 + -2 + 8a Combine like terms: 7 + -2 = 5 7q = 5 + 8a Divide each side by '7'. q = 0.7142857143 + 1.142857143a Simplifying q = 0.7142857143 + 1.142857143a
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