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Simplifying 5(4a + 1) + -1(3a + 2) = 23 + -1(4a + -1) Reorder the terms: 5(1 + 4a) + -1(3a + 2) = 23 + -1(4a + -1) (1 * 5 + 4a * 5) + -1(3a + 2) = 23 + -1(4a + -1) (5 + 20a) + -1(3a + 2) = 23 + -1(4a + -1) Reorder the terms: 5 + 20a + -1(2 + 3a) = 23 + -1(4a + -1) 5 + 20a + (2 * -1 + 3a * -1) = 23 + -1(4a + -1) 5 + 20a + (-2 + -3a) = 23 + -1(4a + -1) Reorder the terms: 5 + -2 + 20a + -3a = 23 + -1(4a + -1) Combine like terms: 5 + -2 = 3 3 + 20a + -3a = 23 + -1(4a + -1) Combine like terms: 20a + -3a = 17a 3 + 17a = 23 + -1(4a + -1) Reorder the terms: 3 + 17a = 23 + -1(-1 + 4a) 3 + 17a = 23 + (-1 * -1 + 4a * -1) 3 + 17a = 23 + (1 + -4a) Combine like terms: 23 + 1 = 24 3 + 17a = 24 + -4a Solving 3 + 17a = 24 + -4a Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '4a' to each side of the equation. 3 + 17a + 4a = 24 + -4a + 4a Combine like terms: 17a + 4a = 21a 3 + 21a = 24 + -4a + 4a Combine like terms: -4a + 4a = 0 3 + 21a = 24 + 0 3 + 21a = 24 Add '-3' to each side of the equation. 3 + -3 + 21a = 24 + -3 Combine like terms: 3 + -3 = 0 0 + 21a = 24 + -3 21a = 24 + -3 Combine like terms: 24 + -3 = 21 21a = 21 Divide each side by '21'. a = 1 Simplifying a = 1
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