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Simplifying 1000 + 5c + 15a + -1(750 + 6c + 8.5a) = 250 + 11c + 23.5a Reorder the terms: 1000 + 5c + 15a + -1(750 + 8.5a + 6c) = 250 + 11c + 23.5a 1000 + 5c + 15a + (750 * -1 + 8.5a * -1 + 6c * -1) = 250 + 11c + 23.5a 1000 + 5c + 15a + (-750 + -8.5a + -6c) = 250 + 11c + 23.5a Reorder the terms: 1000 + -750 + 15a + -8.5a + 5c + -6c = 250 + 11c + 23.5a Combine like terms: 1000 + -750 = 250 250 + 15a + -8.5a + 5c + -6c = 250 + 11c + 23.5a Combine like terms: 15a + -8.5a = 6.5a 250 + 6.5a + 5c + -6c = 250 + 11c + 23.5a Combine like terms: 5c + -6c = -1c 250 + 6.5a + -1c = 250 + 11c + 23.5a Reorder the terms: 250 + 6.5a + -1c = 250 + 23.5a + 11c Add '-250' to each side of the equation. 250 + 6.5a + -250 + -1c = 250 + 23.5a + -250 + 11c Reorder the terms: 250 + -250 + 6.5a + -1c = 250 + 23.5a + -250 + 11c Combine like terms: 250 + -250 = 0 0 + 6.5a + -1c = 250 + 23.5a + -250 + 11c 6.5a + -1c = 250 + 23.5a + -250 + 11c Reorder the terms: 6.5a + -1c = 250 + -250 + 23.5a + 11c Combine like terms: 250 + -250 = 0 6.5a + -1c = 0 + 23.5a + 11c 6.5a + -1c = 23.5a + 11c Solving 6.5a + -1c = 23.5a + 11c Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-23.5a' to each side of the equation. 6.5a + -23.5a + -1c = 23.5a + -23.5a + 11c Combine like terms: 6.5a + -23.5a = -17a -17a + -1c = 23.5a + -23.5a + 11c Combine like terms: 23.5a + -23.5a = 0.0 -17a + -1c = 0.0 + 11c -17a + -1c = 11c Add 'c' to each side of the equation. -17a + -1c + c = 11c + c Combine like terms: -1c + c = 0 -17a + 0 = 11c + c -17a = 11c + c Combine like terms: 11c + c = 12c -17a = 12c Divide each side by '-17'. a = -0.7058823529c Simplifying a = -0.7058823529c
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