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Simplifying 5(a + -1) + -1(2a + -3) = 5(2a + -3) + -1 Reorder the terms: 5(-1 + a) + -1(2a + -3) = 5(2a + -3) + -1 (-1 * 5 + a * 5) + -1(2a + -3) = 5(2a + -3) + -1 (-5 + 5a) + -1(2a + -3) = 5(2a + -3) + -1 Reorder the terms: -5 + 5a + -1(-3 + 2a) = 5(2a + -3) + -1 -5 + 5a + (-3 * -1 + 2a * -1) = 5(2a + -3) + -1 -5 + 5a + (3 + -2a) = 5(2a + -3) + -1 Reorder the terms: -5 + 3 + 5a + -2a = 5(2a + -3) + -1 Combine like terms: -5 + 3 = -2 -2 + 5a + -2a = 5(2a + -3) + -1 Combine like terms: 5a + -2a = 3a -2 + 3a = 5(2a + -3) + -1 Reorder the terms: -2 + 3a = 5(-3 + 2a) + -1 -2 + 3a = (-3 * 5 + 2a * 5) + -1 -2 + 3a = (-15 + 10a) + -1 Reorder the terms: -2 + 3a = -15 + -1 + 10a Combine like terms: -15 + -1 = -16 -2 + 3a = -16 + 10a Solving -2 + 3a = -16 + 10a Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-10a' to each side of the equation. -2 + 3a + -10a = -16 + 10a + -10a Combine like terms: 3a + -10a = -7a -2 + -7a = -16 + 10a + -10a Combine like terms: 10a + -10a = 0 -2 + -7a = -16 + 0 -2 + -7a = -16 Add '2' to each side of the equation. -2 + 2 + -7a = -16 + 2 Combine like terms: -2 + 2 = 0 0 + -7a = -16 + 2 -7a = -16 + 2 Combine like terms: -16 + 2 = -14 -7a = -14 Divide each side by '-7'. a = 2 Simplifying a = 2
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