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Simplifying 45 = 6(a + -8) + 3(6 + -7a) Reorder the terms: 45 = 6(-8 + a) + 3(6 + -7a) 45 = (-8 * 6 + a * 6) + 3(6 + -7a) 45 = (-48 + 6a) + 3(6 + -7a) 45 = -48 + 6a + (6 * 3 + -7a * 3) 45 = -48 + 6a + (18 + -21a) Reorder the terms: 45 = -48 + 18 + 6a + -21a Combine like terms: -48 + 18 = -30 45 = -30 + 6a + -21a Combine like terms: 6a + -21a = -15a 45 = -30 + -15a Solving 45 = -30 + -15a Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '15a' to each side of the equation. 45 + 15a = -30 + -15a + 15a Combine like terms: -15a + 15a = 0 45 + 15a = -30 + 0 45 + 15a = -30 Add '-45' to each side of the equation. 45 + -45 + 15a = -30 + -45 Combine like terms: 45 + -45 = 0 0 + 15a = -30 + -45 15a = -30 + -45 Combine like terms: -30 + -45 = -75 15a = -75 Divide each side by '15'. a = -5 Simplifying a = -5
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