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Simplifying 19 = 7(a + 2) + -4(a + -5) Reorder the terms: 19 = 7(2 + a) + -4(a + -5) 19 = (2 * 7 + a * 7) + -4(a + -5) 19 = (14 + 7a) + -4(a + -5) Reorder the terms: 19 = 14 + 7a + -4(-5 + a) 19 = 14 + 7a + (-5 * -4 + a * -4) 19 = 14 + 7a + (20 + -4a) Reorder the terms: 19 = 14 + 20 + 7a + -4a Combine like terms: 14 + 20 = 34 19 = 34 + 7a + -4a Combine like terms: 7a + -4a = 3a 19 = 34 + 3a Solving 19 = 34 + 3a Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3a' to each side of the equation. 19 + -3a = 34 + 3a + -3a Combine like terms: 3a + -3a = 0 19 + -3a = 34 + 0 19 + -3a = 34 Add '-19' to each side of the equation. 19 + -19 + -3a = 34 + -19 Combine like terms: 19 + -19 = 0 0 + -3a = 34 + -19 -3a = 34 + -19 Combine like terms: 34 + -19 = 15 -3a = 15 Divide each side by '-3'. a = -5 Simplifying a = -5
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