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Simplifying 1a + 2b + 3c + 4d + 5e + 6f + 7g + 6 = 7x Reorder the terms: 6 + 1a + 2b + 3c + 4d + 5e + 6f + 7g = 7x Solving 6 + 1a + 2b + 3c + 4d + 5e + 6f + 7g = 7x Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + 1a + 2b + 3c + 4d + 5e + 6f + -6 + 7g = -6 + 7x Reorder the terms: 6 + -6 + 1a + 2b + 3c + 4d + 5e + 6f + 7g = -6 + 7x Combine like terms: 6 + -6 = 0 0 + 1a + 2b + 3c + 4d + 5e + 6f + 7g = -6 + 7x 1a + 2b + 3c + 4d + 5e + 6f + 7g = -6 + 7x Add '-2b' to each side of the equation. 1a + 2b + 3c + 4d + 5e + 6f + -2b + 7g = -6 + -2b + 7x Reorder the terms: 1a + 2b + -2b + 3c + 4d + 5e + 6f + 7g = -6 + -2b + 7x Combine like terms: 2b + -2b = 0 1a + 0 + 3c + 4d + 5e + 6f + 7g = -6 + -2b + 7x 1a + 3c + 4d + 5e + 6f + 7g = -6 + -2b + 7x Add '-3c' to each side of the equation. 1a + 3c + 4d + 5e + 6f + -3c + 7g = -6 + -2b + -3c + 7x Reorder the terms: 1a + 3c + -3c + 4d + 5e + 6f + 7g = -6 + -2b + -3c + 7x Combine like terms: 3c + -3c = 0 1a + 0 + 4d + 5e + 6f + 7g = -6 + -2b + -3c + 7x 1a + 4d + 5e + 6f + 7g = -6 + -2b + -3c + 7x Add '-4d' to each side of the equation. 1a + 4d + 5e + 6f + -4d + 7g = -6 + -2b + -3c + -4d + 7x Reorder the terms: 1a + 4d + -4d + 5e + 6f + 7g = -6 + -2b + -3c + -4d + 7x Combine like terms: 4d + -4d = 0 1a + 0 + 5e + 6f + 7g = -6 + -2b + -3c + -4d + 7x 1a + 5e + 6f + 7g = -6 + -2b + -3c + -4d + 7x Add '-5e' to each side of the equation. 1a + 5e + 6f + -5e + 7g = -6 + -2b + -3c + -4d + -5e + 7x Reorder the terms: 1a + 5e + -5e + 6f + 7g = -6 + -2b + -3c + -4d + -5e + 7x Combine like terms: 5e + -5e = 0 1a + 0 + 6f + 7g = -6 + -2b + -3c + -4d + -5e + 7x 1a + 6f + 7g = -6 + -2b + -3c + -4d + -5e + 7x Add '-6f' to each side of the equation. 1a + 6f + -6f + 7g = -6 + -2b + -3c + -4d + -5e + -6f + 7x Combine like terms: 6f + -6f = 0 1a + 0 + 7g = -6 + -2b + -3c + -4d + -5e + -6f + 7x 1a + 7g = -6 + -2b + -3c + -4d + -5e + -6f + 7x Add '-7g' to each side of the equation. 1a + 7g + -7g = -6 + -2b + -3c + -4d + -5e + -6f + -7g + 7x Combine like terms: 7g + -7g = 0 1a + 0 = -6 + -2b + -3c + -4d + -5e + -6f + -7g + 7x 1a = -6 + -2b + -3c + -4d + -5e + -6f + -7g + 7x Divide each side by '1'. a = -6 + -2b + -3c + -4d + -5e + -6f + -7g + 7x Simplifying a = -6 + -2b + -3c + -4d + -5e + -6f + -7g + 7x
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