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Simplifying 4x + 5y + 5z + 3a + 3b + 3c + 5d = 82 Reorder the terms: 3a + 3b + 3c + 5d + 4x + 5y + 5z = 82 Solving 3a + 3b + 3c + 5d + 4x + 5y + 5z = 82 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3b' to each side of the equation. 3a + 3b + 3c + 5d + 4x + 5y + -3b + 5z = 82 + -3b Reorder the terms: 3a + 3b + -3b + 3c + 5d + 4x + 5y + 5z = 82 + -3b Combine like terms: 3b + -3b = 0 3a + 0 + 3c + 5d + 4x + 5y + 5z = 82 + -3b 3a + 3c + 5d + 4x + 5y + 5z = 82 + -3b Add '-3c' to each side of the equation. 3a + 3c + 5d + 4x + 5y + -3c + 5z = 82 + -3b + -3c Reorder the terms: 3a + 3c + -3c + 5d + 4x + 5y + 5z = 82 + -3b + -3c Combine like terms: 3c + -3c = 0 3a + 0 + 5d + 4x + 5y + 5z = 82 + -3b + -3c 3a + 5d + 4x + 5y + 5z = 82 + -3b + -3c Add '-5d' to each side of the equation. 3a + 5d + 4x + 5y + -5d + 5z = 82 + -3b + -3c + -5d Reorder the terms: 3a + 5d + -5d + 4x + 5y + 5z = 82 + -3b + -3c + -5d Combine like terms: 5d + -5d = 0 3a + 0 + 4x + 5y + 5z = 82 + -3b + -3c + -5d 3a + 4x + 5y + 5z = 82 + -3b + -3c + -5d Add '-4x' to each side of the equation. 3a + 4x + 5y + -4x + 5z = 82 + -3b + -3c + -5d + -4x Reorder the terms: 3a + 4x + -4x + 5y + 5z = 82 + -3b + -3c + -5d + -4x Combine like terms: 4x + -4x = 0 3a + 0 + 5y + 5z = 82 + -3b + -3c + -5d + -4x 3a + 5y + 5z = 82 + -3b + -3c + -5d + -4x Add '-5y' to each side of the equation. 3a + 5y + -5y + 5z = 82 + -3b + -3c + -5d + -4x + -5y Combine like terms: 5y + -5y = 0 3a + 0 + 5z = 82 + -3b + -3c + -5d + -4x + -5y 3a + 5z = 82 + -3b + -3c + -5d + -4x + -5y Add '-5z' to each side of the equation. 3a + 5z + -5z = 82 + -3b + -3c + -5d + -4x + -5y + -5z Combine like terms: 5z + -5z = 0 3a + 0 = 82 + -3b + -3c + -5d + -4x + -5y + -5z 3a = 82 + -3b + -3c + -5d + -4x + -5y + -5z Divide each side by '3'. a = 27.33333333 + -1b + -1c + -1.666666667d + -1.333333333x + -1.666666667y + -1.666666667z Simplifying a = 27.33333333 + -1b + -1c + -1.666666667d + -1.333333333x + -1.666666667y + -1.666666667z
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