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Simplifying 5(7 + -1a) + -3(a + 4) + -4 = (a + -3) + 7 (7 * 5 + -1a * 5) + -3(a + 4) + -4 = (a + -3) + 7 (35 + -5a) + -3(a + 4) + -4 = (a + -3) + 7 Reorder the terms: 35 + -5a + -3(4 + a) + -4 = (a + -3) + 7 35 + -5a + (4 * -3 + a * -3) + -4 = (a + -3) + 7 35 + -5a + (-12 + -3a) + -4 = (a + -3) + 7 Reorder the terms: 35 + -12 + -4 + -5a + -3a = (a + -3) + 7 Combine like terms: 35 + -12 = 23 23 + -4 + -5a + -3a = (a + -3) + 7 Combine like terms: 23 + -4 = 19 19 + -5a + -3a = (a + -3) + 7 Combine like terms: -5a + -3a = -8a 19 + -8a = (a + -3) + 7 Reorder the terms: 19 + -8a = (-3 + a) + 7 Remove parenthesis around (-3 + a) 19 + -8a = -3 + a + 7 Reorder the terms: 19 + -8a = -3 + 7 + a Combine like terms: -3 + 7 = 4 19 + -8a = 4 + a Solving 19 + -8a = 4 + a Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1a' to each side of the equation. 19 + -8a + -1a = 4 + a + -1a Combine like terms: -8a + -1a = -9a 19 + -9a = 4 + a + -1a Combine like terms: a + -1a = 0 19 + -9a = 4 + 0 19 + -9a = 4 Add '-19' to each side of the equation. 19 + -19 + -9a = 4 + -19 Combine like terms: 19 + -19 = 0 0 + -9a = 4 + -19 -9a = 4 + -19 Combine like terms: 4 + -19 = -15 -9a = -15 Divide each side by '-9'. a = 1.666666667 Simplifying a = 1.666666667
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