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Simplifying (7a + -2b + 19) + (13a + 5b + -12) = 0 Reorder the terms: (19 + 7a + -2b) + (13a + 5b + -12) = 0 Remove parenthesis around (19 + 7a + -2b) 19 + 7a + -2b + (13a + 5b + -12) = 0 Reorder the terms: 19 + 7a + -2b + (-12 + 13a + 5b) = 0 Remove parenthesis around (-12 + 13a + 5b) 19 + 7a + -2b + -12 + 13a + 5b = 0 Reorder the terms: 19 + -12 + 7a + 13a + -2b + 5b = 0 Combine like terms: 19 + -12 = 7 7 + 7a + 13a + -2b + 5b = 0 Combine like terms: 7a + 13a = 20a 7 + 20a + -2b + 5b = 0 Combine like terms: -2b + 5b = 3b 7 + 20a + 3b = 0 Solving 7 + 20a + 3b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + 20a + -7 + 3b = 0 + -7 Reorder the terms: 7 + -7 + 20a + 3b = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 20a + 3b = 0 + -7 20a + 3b = 0 + -7 Combine like terms: 0 + -7 = -7 20a + 3b = -7 Add '-3b' to each side of the equation. 20a + 3b + -3b = -7 + -3b Combine like terms: 3b + -3b = 0 20a + 0 = -7 + -3b 20a = -7 + -3b Divide each side by '20'. a = -0.35 + -0.15b Simplifying a = -0.35 + -0.15b
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