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Simplifying 8(a + 2) + -3(a + -4) = 6(a + -7) + 8 Reorder the terms: 8(2 + a) + -3(a + -4) = 6(a + -7) + 8 (2 * 8 + a * 8) + -3(a + -4) = 6(a + -7) + 8 (16 + 8a) + -3(a + -4) = 6(a + -7) + 8 Reorder the terms: 16 + 8a + -3(-4 + a) = 6(a + -7) + 8 16 + 8a + (-4 * -3 + a * -3) = 6(a + -7) + 8 16 + 8a + (12 + -3a) = 6(a + -7) + 8 Reorder the terms: 16 + 12 + 8a + -3a = 6(a + -7) + 8 Combine like terms: 16 + 12 = 28 28 + 8a + -3a = 6(a + -7) + 8 Combine like terms: 8a + -3a = 5a 28 + 5a = 6(a + -7) + 8 Reorder the terms: 28 + 5a = 6(-7 + a) + 8 28 + 5a = (-7 * 6 + a * 6) + 8 28 + 5a = (-42 + 6a) + 8 Reorder the terms: 28 + 5a = -42 + 8 + 6a Combine like terms: -42 + 8 = -34 28 + 5a = -34 + 6a Solving 28 + 5a = -34 + 6a Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-6a' to each side of the equation. 28 + 5a + -6a = -34 + 6a + -6a Combine like terms: 5a + -6a = -1a 28 + -1a = -34 + 6a + -6a Combine like terms: 6a + -6a = 0 28 + -1a = -34 + 0 28 + -1a = -34 Add '-28' to each side of the equation. 28 + -28 + -1a = -34 + -28 Combine like terms: 28 + -28 = 0 0 + -1a = -34 + -28 -1a = -34 + -28 Combine like terms: -34 + -28 = -62 -1a = -62 Divide each side by '-1'. a = 62 Simplifying a = 62
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