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Simplifying 5(a + 1) + 2 = 2(a + -4) + 19 Reorder the terms: 5(1 + a) + 2 = 2(a + -4) + 19 (1 * 5 + a * 5) + 2 = 2(a + -4) + 19 (5 + 5a) + 2 = 2(a + -4) + 19 Reorder the terms: 5 + 2 + 5a = 2(a + -4) + 19 Combine like terms: 5 + 2 = 7 7 + 5a = 2(a + -4) + 19 Reorder the terms: 7 + 5a = 2(-4 + a) + 19 7 + 5a = (-4 * 2 + a * 2) + 19 7 + 5a = (-8 + 2a) + 19 Reorder the terms: 7 + 5a = -8 + 19 + 2a Combine like terms: -8 + 19 = 11 7 + 5a = 11 + 2a Solving 7 + 5a = 11 + 2a Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2a' to each side of the equation. 7 + 5a + -2a = 11 + 2a + -2a Combine like terms: 5a + -2a = 3a 7 + 3a = 11 + 2a + -2a Combine like terms: 2a + -2a = 0 7 + 3a = 11 + 0 7 + 3a = 11 Add '-7' to each side of the equation. 7 + -7 + 3a = 11 + -7 Combine like terms: 7 + -7 = 0 0 + 3a = 11 + -7 3a = 11 + -7 Combine like terms: 11 + -7 = 4 3a = 4 Divide each side by '3'. a = 1.333333333 Simplifying a = 1.333333333
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