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Simplifying y + -1[5 + -3b + -1(7y + -4a)] = r Reorder the terms: y + -1[5 + -3b + -1(-4a + 7y)] = r y + -1[5 + -3b + (-4a * -1 + 7y * -1)] = r y + -1[5 + -3b + (4a + -7y)] = r Reorder the terms: y + -1[5 + 4a + -3b + -7y] = r y + [5 * -1 + 4a * -1 + -3b * -1 + -7y * -1] = r y + [-5 + -4a + 3b + 7y] = r Reorder the terms: -5 + -4a + 3b + y + 7y = r Combine like terms: y + 7y = 8y -5 + -4a + 3b + 8y = r Solving -5 + -4a + 3b + 8y = r Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '5' to each side of the equation. -5 + -4a + 3b + 5 + 8y = 5 + r Reorder the terms: -5 + 5 + -4a + 3b + 8y = 5 + r Combine like terms: -5 + 5 = 0 0 + -4a + 3b + 8y = 5 + r -4a + 3b + 8y = 5 + r Add '-3b' to each side of the equation. -4a + 3b + -3b + 8y = 5 + -3b + r Combine like terms: 3b + -3b = 0 -4a + 0 + 8y = 5 + -3b + r -4a + 8y = 5 + -3b + r Add '-8y' to each side of the equation. -4a + 8y + -8y = 5 + -3b + r + -8y Combine like terms: 8y + -8y = 0 -4a + 0 = 5 + -3b + r + -8y -4a = 5 + -3b + r + -8y Divide each side by '-4'. a = -1.25 + 0.75b + -0.25r + 2y Simplifying a = -1.25 + 0.75b + -0.25r + 2y
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