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Simplifying 5x + -1(7a + -8b) + -3x + 5y + -42 = 0 5x + (7a * -1 + -8b * -1) + -3x + 5y + -42 = 0 5x + (-7a + 8b) + -3x + 5y + -42 = 0 Reorder the terms: -42 + -7a + 8b + 5x + -3x + 5y = 0 Combine like terms: 5x + -3x = 2x -42 + -7a + 8b + 2x + 5y = 0 Solving -42 + -7a + 8b + 2x + 5y = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '42' to each side of the equation. -42 + -7a + 8b + 2x + 42 + 5y = 0 + 42 Reorder the terms: -42 + 42 + -7a + 8b + 2x + 5y = 0 + 42 Combine like terms: -42 + 42 = 0 0 + -7a + 8b + 2x + 5y = 0 + 42 -7a + 8b + 2x + 5y = 0 + 42 Combine like terms: 0 + 42 = 42 -7a + 8b + 2x + 5y = 42 Add '-8b' to each side of the equation. -7a + 8b + 2x + -8b + 5y = 42 + -8b Reorder the terms: -7a + 8b + -8b + 2x + 5y = 42 + -8b Combine like terms: 8b + -8b = 0 -7a + 0 + 2x + 5y = 42 + -8b -7a + 2x + 5y = 42 + -8b Add '-2x' to each side of the equation. -7a + 2x + -2x + 5y = 42 + -8b + -2x Combine like terms: 2x + -2x = 0 -7a + 0 + 5y = 42 + -8b + -2x -7a + 5y = 42 + -8b + -2x Add '-5y' to each side of the equation. -7a + 5y + -5y = 42 + -8b + -2x + -5y Combine like terms: 5y + -5y = 0 -7a + 0 = 42 + -8b + -2x + -5y -7a = 42 + -8b + -2x + -5y Divide each side by '-7'. a = -6 + 1.142857143b + 0.2857142857x + 0.7142857143y Simplifying a = -6 + 1.142857143b + 0.2857142857x + 0.7142857143y
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