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Simplifying j + -1k + -1o + -4 + -1f + -1a + -7 + -1a + -1d + -1v + -1f + -1g = 123 Reorder the terms: -4 + -7 + -1a + -1a + -1d + -1f + -1f + -1g + j + -1k + -1o + -1v = 123 Combine like terms: -4 + -7 = -11 -11 + -1a + -1a + -1d + -1f + -1f + -1g + j + -1k + -1o + -1v = 123 Combine like terms: -1a + -1a = -2a -11 + -2a + -1d + -1f + -1f + -1g + j + -1k + -1o + -1v = 123 Combine like terms: -1f + -1f = -2f -11 + -2a + -1d + -2f + -1g + j + -1k + -1o + -1v = 123 Solving -11 + -2a + -1d + -2f + -1g + j + -1k + -1o + -1v = 123 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '11' to each side of the equation. -11 + -2a + -1d + -2f + -1g + j + -1k + -1o + 11 + -1v = 123 + 11 Reorder the terms: -11 + 11 + -2a + -1d + -2f + -1g + j + -1k + -1o + -1v = 123 + 11 Combine like terms: -11 + 11 = 0 0 + -2a + -1d + -2f + -1g + j + -1k + -1o + -1v = 123 + 11 -2a + -1d + -2f + -1g + j + -1k + -1o + -1v = 123 + 11 Combine like terms: 123 + 11 = 134 -2a + -1d + -2f + -1g + j + -1k + -1o + -1v = 134 Add 'd' to each side of the equation. -2a + -1d + -2f + -1g + j + -1k + -1o + d + -1v = 134 + d Reorder the terms: -2a + -1d + d + -2f + -1g + j + -1k + -1o + -1v = 134 + d Combine like terms: -1d + d = 0 -2a + 0 + -2f + -1g + j + -1k + -1o + -1v = 134 + d -2a + -2f + -1g + j + -1k + -1o + -1v = 134 + d Add '2f' to each side of the equation. -2a + -2f + -1g + j + -1k + -1o + 2f + -1v = 134 + d + 2f Reorder the terms: -2a + -2f + 2f + -1g + j + -1k + -1o + -1v = 134 + d + 2f Combine like terms: -2f + 2f = 0 -2a + 0 + -1g + j + -1k + -1o + -1v = 134 + d + 2f -2a + -1g + j + -1k + -1o + -1v = 134 + d + 2f Add 'g' to each side of the equation. -2a + -1g + j + -1k + -1o + g + -1v = 134 + d + 2f + g Reorder the terms: -2a + -1g + g + j + -1k + -1o + -1v = 134 + d + 2f + g Combine like terms: -1g + g = 0 -2a + 0 + j + -1k + -1o + -1v = 134 + d + 2f + g -2a + j + -1k + -1o + -1v = 134 + d + 2f + g Add '-1j' to each side of the equation. -2a + j + -1k + -1o + -1j + -1v = 134 + d + 2f + g + -1j Reorder the terms: -2a + j + -1j + -1k + -1o + -1v = 134 + d + 2f + g + -1j Combine like terms: j + -1j = 0 -2a + 0 + -1k + -1o + -1v = 134 + d + 2f + g + -1j -2a + -1k + -1o + -1v = 134 + d + 2f + g + -1j Add 'k' to each side of the equation. -2a + -1k + -1o + k + -1v = 134 + d + 2f + g + -1j + k Reorder the terms: -2a + -1k + k + -1o + -1v = 134 + d + 2f + g + -1j + k Combine like terms: -1k + k = 0 -2a + 0 + -1o + -1v = 134 + d + 2f + g + -1j + k -2a + -1o + -1v = 134 + d + 2f + g + -1j + k Add 'o' to each side of the equation. -2a + -1o + o + -1v = 134 + d + 2f + g + -1j + k + o Combine like terms: -1o + o = 0 -2a + 0 + -1v = 134 + d + 2f + g + -1j + k + o -2a + -1v = 134 + d + 2f + g + -1j + k + o Add 'v' to each side of the equation. -2a + -1v + v = 134 + d + 2f + g + -1j + k + o + v Combine like terms: -1v + v = 0 -2a + 0 = 134 + d + 2f + g + -1j + k + o + v -2a = 134 + d + 2f + g + -1j + k + o + v Divide each side by '-2'. a = -67 + -0.5d + -1f + -0.5g + 0.5j + -0.5k + -0.5o + -0.5v Simplifying a = -67 + -0.5d + -1f + -0.5g + 0.5j + -0.5k + -0.5o + -0.5v
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