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Simplifying -8a + -4b + 18a + -5c + 2c + -12b + e + -45d + 4c = 0 Reorder the terms: -8a + 18a + -4b + -12b + -5c + 2c + 4c + -45d + e = 0 Combine like terms: -8a + 18a = 10a 10a + -4b + -12b + -5c + 2c + 4c + -45d + e = 0 Combine like terms: -4b + -12b = -16b 10a + -16b + -5c + 2c + 4c + -45d + e = 0 Combine like terms: -5c + 2c = -3c 10a + -16b + -3c + 4c + -45d + e = 0 Combine like terms: -3c + 4c = 1c 10a + -16b + 1c + -45d + e = 0 Solving 10a + -16b + 1c + -45d + e = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '16b' to each side of the equation. 10a + -16b + 1c + -45d + 16b + e = 0 + 16b Reorder the terms: 10a + -16b + 16b + 1c + -45d + e = 0 + 16b Combine like terms: -16b + 16b = 0 10a + 0 + 1c + -45d + e = 0 + 16b 10a + 1c + -45d + e = 0 + 16b Remove the zero: 10a + 1c + -45d + e = 16b Add '-1c' to each side of the equation. 10a + 1c + -45d + -1c + e = 16b + -1c Reorder the terms: 10a + 1c + -1c + -45d + e = 16b + -1c Combine like terms: 1c + -1c = 0 10a + 0 + -45d + e = 16b + -1c 10a + -45d + e = 16b + -1c Add '45d' to each side of the equation. 10a + -45d + 45d + e = 16b + -1c + 45d Combine like terms: -45d + 45d = 0 10a + 0 + e = 16b + -1c + 45d 10a + e = 16b + -1c + 45d Add '-1e' to each side of the equation. 10a + e + -1e = 16b + -1c + 45d + -1e Combine like terms: e + -1e = 0 10a + 0 = 16b + -1c + 45d + -1e 10a = 16b + -1c + 45d + -1e Divide each side by '10'. a = 1.6b + -0.1c + 4.5d + -0.1e Simplifying a = 1.6b + -0.1c + 4.5d + -0.1e
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