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Simplifying 5(a + b) + 3(b + c) = 4(b + -1c) (a * 5 + b * 5) + 3(b + c) = 4(b + -1c) (5a + 5b) + 3(b + c) = 4(b + -1c) 5a + 5b + (b * 3 + c * 3) = 4(b + -1c) 5a + 5b + (3b + 3c) = 4(b + -1c) Combine like terms: 5b + 3b = 8b 5a + 8b + 3c = 4(b + -1c) 5a + 8b + 3c = (b * 4 + -1c * 4) 5a + 8b + 3c = (4b + -4c) Solving 5a + 8b + 3c = 4b + -4c Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-8b' to each side of the equation. 5a + 8b + -8b + 3c = 4b + -8b + -4c Combine like terms: 8b + -8b = 0 5a + 0 + 3c = 4b + -8b + -4c 5a + 3c = 4b + -8b + -4c Combine like terms: 4b + -8b = -4b 5a + 3c = -4b + -4c Add '-3c' to each side of the equation. 5a + 3c + -3c = -4b + -4c + -3c Combine like terms: 3c + -3c = 0 5a + 0 = -4b + -4c + -3c 5a = -4b + -4c + -3c Combine like terms: -4c + -3c = -7c 5a = -4b + -7c Divide each side by '5'. a = -0.8b + -1.4c Simplifying a = -0.8b + -1.4c
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