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Simplifying 6(a + 3) = 21 + -31(1 + -2a) Reorder the terms: 6(3 + a) = 21 + -31(1 + -2a) (3 * 6 + a * 6) = 21 + -31(1 + -2a) (18 + 6a) = 21 + -31(1 + -2a) 18 + 6a = 21 + (1 * -31 + -2a * -31) 18 + 6a = 21 + (-31 + 62a) Combine like terms: 21 + -31 = -10 18 + 6a = -10 + 62a Solving 18 + 6a = -10 + 62a Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-62a' to each side of the equation. 18 + 6a + -62a = -10 + 62a + -62a Combine like terms: 6a + -62a = -56a 18 + -56a = -10 + 62a + -62a Combine like terms: 62a + -62a = 0 18 + -56a = -10 + 0 18 + -56a = -10 Add '-18' to each side of the equation. 18 + -18 + -56a = -10 + -18 Combine like terms: 18 + -18 = 0 0 + -56a = -10 + -18 -56a = -10 + -18 Combine like terms: -10 + -18 = -28 -56a = -28 Divide each side by '-56'. a = 0.5 Simplifying a = 0.5
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