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Simplifying 5(a + -3) + 2(a + 4) = 3(a + -1) Reorder the terms: 5(-3 + a) + 2(a + 4) = 3(a + -1) (-3 * 5 + a * 5) + 2(a + 4) = 3(a + -1) (-15 + 5a) + 2(a + 4) = 3(a + -1) Reorder the terms: -15 + 5a + 2(4 + a) = 3(a + -1) -15 + 5a + (4 * 2 + a * 2) = 3(a + -1) -15 + 5a + (8 + 2a) = 3(a + -1) Reorder the terms: -15 + 8 + 5a + 2a = 3(a + -1) Combine like terms: -15 + 8 = -7 -7 + 5a + 2a = 3(a + -1) Combine like terms: 5a + 2a = 7a -7 + 7a = 3(a + -1) Reorder the terms: -7 + 7a = 3(-1 + a) -7 + 7a = (-1 * 3 + a * 3) -7 + 7a = (-3 + 3a) Solving -7 + 7a = -3 + 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. -7 + 7a + -3a = -3 + 3a + -3a Combine like terms: 7a + -3a = 4a -7 + 4a = -3 + 3a + -3a Combine like terms: 3a + -3a = 0 -7 + 4a = -3 + 0 -7 + 4a = -3 Add '7' to each side of the equation. -7 + 7 + 4a = -3 + 7 Combine like terms: -7 + 7 = 0 0 + 4a = -3 + 7 4a = -3 + 7 Combine like terms: -3 + 7 = 4 4a = 4 Divide each side by '4'. a = 1 Simplifying a = 1
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