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Simplifying 1a + 2b + 3c + 4d + 5e + 6f + 7g + 8h + 9i + 10j = 1000 Solving 1a + 2b + 3c + 4d + 5e + 6f + 7g + 8h + 9i + 10j = 1000 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2b' to each side of the equation. 1a + 2b + 3c + 4d + 5e + 6f + 7g + 8h + 9i + -2b + 10j = 1000 + -2b Reorder the terms: 1a + 2b + -2b + 3c + 4d + 5e + 6f + 7g + 8h + 9i + 10j = 1000 + -2b Combine like terms: 2b + -2b = 0 1a + 0 + 3c + 4d + 5e + 6f + 7g + 8h + 9i + 10j = 1000 + -2b 1a + 3c + 4d + 5e + 6f + 7g + 8h + 9i + 10j = 1000 + -2b Add '-3c' to each side of the equation. 1a + 3c + 4d + 5e + 6f + 7g + 8h + 9i + -3c + 10j = 1000 + -2b + -3c Reorder the terms: 1a + 3c + -3c + 4d + 5e + 6f + 7g + 8h + 9i + 10j = 1000 + -2b + -3c Combine like terms: 3c + -3c = 0 1a + 0 + 4d + 5e + 6f + 7g + 8h + 9i + 10j = 1000 + -2b + -3c 1a + 4d + 5e + 6f + 7g + 8h + 9i + 10j = 1000 + -2b + -3c Add '-4d' to each side of the equation. 1a + 4d + 5e + 6f + 7g + 8h + 9i + -4d + 10j = 1000 + -2b + -3c + -4d Reorder the terms: 1a + 4d + -4d + 5e + 6f + 7g + 8h + 9i + 10j = 1000 + -2b + -3c + -4d Combine like terms: 4d + -4d = 0 1a + 0 + 5e + 6f + 7g + 8h + 9i + 10j = 1000 + -2b + -3c + -4d 1a + 5e + 6f + 7g + 8h + 9i + 10j = 1000 + -2b + -3c + -4d Add '-5e' to each side of the equation. 1a + 5e + 6f + 7g + 8h + 9i + -5e + 10j = 1000 + -2b + -3c + -4d + -5e Reorder the terms: 1a + 5e + -5e + 6f + 7g + 8h + 9i + 10j = 1000 + -2b + -3c + -4d + -5e Combine like terms: 5e + -5e = 0 1a + 0 + 6f + 7g + 8h + 9i + 10j = 1000 + -2b + -3c + -4d + -5e 1a + 6f + 7g + 8h + 9i + 10j = 1000 + -2b + -3c + -4d + -5e Add '-6f' to each side of the equation. 1a + 6f + 7g + 8h + 9i + -6f + 10j = 1000 + -2b + -3c + -4d + -5e + -6f Reorder the terms: 1a + 6f + -6f + 7g + 8h + 9i + 10j = 1000 + -2b + -3c + -4d + -5e + -6f Combine like terms: 6f + -6f = 0 1a + 0 + 7g + 8h + 9i + 10j = 1000 + -2b + -3c + -4d + -5e + -6f 1a + 7g + 8h + 9i + 10j = 1000 + -2b + -3c + -4d + -5e + -6f Add '-7g' to each side of the equation. 1a + 7g + 8h + 9i + -7g + 10j = 1000 + -2b + -3c + -4d + -5e + -6f + -7g Reorder the terms: 1a + 7g + -7g + 8h + 9i + 10j = 1000 + -2b + -3c + -4d + -5e + -6f + -7g Combine like terms: 7g + -7g = 0 1a + 0 + 8h + 9i + 10j = 1000 + -2b + -3c + -4d + -5e + -6f + -7g 1a + 8h + 9i + 10j = 1000 + -2b + -3c + -4d + -5e + -6f + -7g Add '-8h' to each side of the equation. 1a + 8h + 9i + -8h + 10j = 1000 + -2b + -3c + -4d + -5e + -6f + -7g + -8h Reorder the terms: 1a + 8h + -8h + 9i + 10j = 1000 + -2b + -3c + -4d + -5e + -6f + -7g + -8h Combine like terms: 8h + -8h = 0 1a + 0 + 9i + 10j = 1000 + -2b + -3c + -4d + -5e + -6f + -7g + -8h 1a + 9i + 10j = 1000 + -2b + -3c + -4d + -5e + -6f + -7g + -8h Add '-9i' to each side of the equation. 1a + 9i + -9i + 10j = 1000 + -2b + -3c + -4d + -5e + -6f + -7g + -8h + -9i Combine like terms: 9i + -9i = 0 1a + 0 + 10j = 1000 + -2b + -3c + -4d + -5e + -6f + -7g + -8h + -9i 1a + 10j = 1000 + -2b + -3c + -4d + -5e + -6f + -7g + -8h + -9i Add '-10j' to each side of the equation. 1a + 10j + -10j = 1000 + -2b + -3c + -4d + -5e + -6f + -7g + -8h + -9i + -10j Combine like terms: 10j + -10j = 0 1a + 0 = 1000 + -2b + -3c + -4d + -5e + -6f + -7g + -8h + -9i + -10j 1a = 1000 + -2b + -3c + -4d + -5e + -6f + -7g + -8h + -9i + -10j Divide each side by '1'. a = 1000 + -2b + -3c + -4d + -5e + -6f + -7g + -8h + -9i + -10j Simplifying a = 1000 + -2b + -3c + -4d + -5e + -6f + -7g + -8h + -9i + -10j
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