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Simplifying 5(a + 2) + -3(2a + 5) = 17a + -2(5a + 1) + 5(a + -1) Reorder the terms: 5(2 + a) + -3(2a + 5) = 17a + -2(5a + 1) + 5(a + -1) (2 * 5 + a * 5) + -3(2a + 5) = 17a + -2(5a + 1) + 5(a + -1) (10 + 5a) + -3(2a + 5) = 17a + -2(5a + 1) + 5(a + -1) Reorder the terms: 10 + 5a + -3(5 + 2a) = 17a + -2(5a + 1) + 5(a + -1) 10 + 5a + (5 * -3 + 2a * -3) = 17a + -2(5a + 1) + 5(a + -1) 10 + 5a + (-15 + -6a) = 17a + -2(5a + 1) + 5(a + -1) Reorder the terms: 10 + -15 + 5a + -6a = 17a + -2(5a + 1) + 5(a + -1) Combine like terms: 10 + -15 = -5 -5 + 5a + -6a = 17a + -2(5a + 1) + 5(a + -1) Combine like terms: 5a + -6a = -1a -5 + -1a = 17a + -2(5a + 1) + 5(a + -1) Reorder the terms: -5 + -1a = 17a + -2(1 + 5a) + 5(a + -1) -5 + -1a = 17a + (1 * -2 + 5a * -2) + 5(a + -1) -5 + -1a = 17a + (-2 + -10a) + 5(a + -1) Reorder the terms: -5 + -1a = 17a + -2 + -10a + 5(-1 + a) -5 + -1a = 17a + -2 + -10a + (-1 * 5 + a * 5) -5 + -1a = 17a + -2 + -10a + (-5 + 5a) Reorder the terms: -5 + -1a = -2 + -5 + 17a + -10a + 5a Combine like terms: -2 + -5 = -7 -5 + -1a = -7 + 17a + -10a + 5a Combine like terms: 17a + -10a = 7a -5 + -1a = -7 + 7a + 5a Combine like terms: 7a + 5a = 12a -5 + -1a = -7 + 12a Solving -5 + -1a = -7 + 12a Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-12a' to each side of the equation. -5 + -1a + -12a = -7 + 12a + -12a Combine like terms: -1a + -12a = -13a -5 + -13a = -7 + 12a + -12a Combine like terms: 12a + -12a = 0 -5 + -13a = -7 + 0 -5 + -13a = -7 Add '5' to each side of the equation. -5 + 5 + -13a = -7 + 5 Combine like terms: -5 + 5 = 0 0 + -13a = -7 + 5 -13a = -7 + 5 Combine like terms: -7 + 5 = -2 -13a = -2 Divide each side by '-13'. a = 0.1538461538 Simplifying a = 0.1538461538
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