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Simplifying 10a + 9b + 8c + 7d + 6e + 5f + 4g + 3h + 2i + 1j = 135 Solving 10a + 9b + 8c + 7d + 6e + 5f + 4g + 3h + 2i + 1j = 135 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-9b' to each side of the equation. 10a + 9b + 8c + 7d + 6e + 5f + 4g + 3h + 2i + -9b + 1j = 135 + -9b Reorder the terms: 10a + 9b + -9b + 8c + 7d + 6e + 5f + 4g + 3h + 2i + 1j = 135 + -9b Combine like terms: 9b + -9b = 0 10a + 0 + 8c + 7d + 6e + 5f + 4g + 3h + 2i + 1j = 135 + -9b 10a + 8c + 7d + 6e + 5f + 4g + 3h + 2i + 1j = 135 + -9b Add '-8c' to each side of the equation. 10a + 8c + 7d + 6e + 5f + 4g + 3h + 2i + -8c + 1j = 135 + -9b + -8c Reorder the terms: 10a + 8c + -8c + 7d + 6e + 5f + 4g + 3h + 2i + 1j = 135 + -9b + -8c Combine like terms: 8c + -8c = 0 10a + 0 + 7d + 6e + 5f + 4g + 3h + 2i + 1j = 135 + -9b + -8c 10a + 7d + 6e + 5f + 4g + 3h + 2i + 1j = 135 + -9b + -8c Add '-7d' to each side of the equation. 10a + 7d + 6e + 5f + 4g + 3h + 2i + -7d + 1j = 135 + -9b + -8c + -7d Reorder the terms: 10a + 7d + -7d + 6e + 5f + 4g + 3h + 2i + 1j = 135 + -9b + -8c + -7d Combine like terms: 7d + -7d = 0 10a + 0 + 6e + 5f + 4g + 3h + 2i + 1j = 135 + -9b + -8c + -7d 10a + 6e + 5f + 4g + 3h + 2i + 1j = 135 + -9b + -8c + -7d Add '-6e' to each side of the equation. 10a + 6e + 5f + 4g + 3h + 2i + -6e + 1j = 135 + -9b + -8c + -7d + -6e Reorder the terms: 10a + 6e + -6e + 5f + 4g + 3h + 2i + 1j = 135 + -9b + -8c + -7d + -6e Combine like terms: 6e + -6e = 0 10a + 0 + 5f + 4g + 3h + 2i + 1j = 135 + -9b + -8c + -7d + -6e 10a + 5f + 4g + 3h + 2i + 1j = 135 + -9b + -8c + -7d + -6e Add '-5f' to each side of the equation. 10a + 5f + 4g + 3h + 2i + -5f + 1j = 135 + -9b + -8c + -7d + -6e + -5f Reorder the terms: 10a + 5f + -5f + 4g + 3h + 2i + 1j = 135 + -9b + -8c + -7d + -6e + -5f Combine like terms: 5f + -5f = 0 10a + 0 + 4g + 3h + 2i + 1j = 135 + -9b + -8c + -7d + -6e + -5f 10a + 4g + 3h + 2i + 1j = 135 + -9b + -8c + -7d + -6e + -5f Add '-4g' to each side of the equation. 10a + 4g + 3h + 2i + -4g + 1j = 135 + -9b + -8c + -7d + -6e + -5f + -4g Reorder the terms: 10a + 4g + -4g + 3h + 2i + 1j = 135 + -9b + -8c + -7d + -6e + -5f + -4g Combine like terms: 4g + -4g = 0 10a + 0 + 3h + 2i + 1j = 135 + -9b + -8c + -7d + -6e + -5f + -4g 10a + 3h + 2i + 1j = 135 + -9b + -8c + -7d + -6e + -5f + -4g Add '-3h' to each side of the equation. 10a + 3h + 2i + -3h + 1j = 135 + -9b + -8c + -7d + -6e + -5f + -4g + -3h Reorder the terms: 10a + 3h + -3h + 2i + 1j = 135 + -9b + -8c + -7d + -6e + -5f + -4g + -3h Combine like terms: 3h + -3h = 0 10a + 0 + 2i + 1j = 135 + -9b + -8c + -7d + -6e + -5f + -4g + -3h 10a + 2i + 1j = 135 + -9b + -8c + -7d + -6e + -5f + -4g + -3h Add '-2i' to each side of the equation. 10a + 2i + -2i + 1j = 135 + -9b + -8c + -7d + -6e + -5f + -4g + -3h + -2i Combine like terms: 2i + -2i = 0 10a + 0 + 1j = 135 + -9b + -8c + -7d + -6e + -5f + -4g + -3h + -2i 10a + 1j = 135 + -9b + -8c + -7d + -6e + -5f + -4g + -3h + -2i Add '-1j' to each side of the equation. 10a + 1j + -1j = 135 + -9b + -8c + -7d + -6e + -5f + -4g + -3h + -2i + -1j Combine like terms: 1j + -1j = 0 10a + 0 = 135 + -9b + -8c + -7d + -6e + -5f + -4g + -3h + -2i + -1j 10a = 135 + -9b + -8c + -7d + -6e + -5f + -4g + -3h + -2i + -1j Divide each side by '10'. a = 13.5 + -0.9b + -0.8c + -0.7d + -0.6e + -0.5f + -0.4g + -0.3h + -0.2i + -0.1j Simplifying a = 13.5 + -0.9b + -0.8c + -0.7d + -0.6e + -0.5f + -0.4g + -0.3h + -0.2i + -0.1j
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