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Simplifying -6(x + 8) + 8(6x + 9) = 41(x + 1) + -8 Reorder the terms: -6(8 + x) + 8(6x + 9) = 41(x + 1) + -8 (8 * -6 + x * -6) + 8(6x + 9) = 41(x + 1) + -8 (-48 + -6x) + 8(6x + 9) = 41(x + 1) + -8 Reorder the terms: -48 + -6x + 8(9 + 6x) = 41(x + 1) + -8 -48 + -6x + (9 * 8 + 6x * 8) = 41(x + 1) + -8 -48 + -6x + (72 + 48x) = 41(x + 1) + -8 Reorder the terms: -48 + 72 + -6x + 48x = 41(x + 1) + -8 Combine like terms: -48 + 72 = 24 24 + -6x + 48x = 41(x + 1) + -8 Combine like terms: -6x + 48x = 42x 24 + 42x = 41(x + 1) + -8 Reorder the terms: 24 + 42x = 41(1 + x) + -8 24 + 42x = (1 * 41 + x * 41) + -8 24 + 42x = (41 + 41x) + -8 Reorder the terms: 24 + 42x = 41 + -8 + 41x Combine like terms: 41 + -8 = 33 24 + 42x = 33 + 41x Solving 24 + 42x = 33 + 41x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-41x' to each side of the equation. 24 + 42x + -41x = 33 + 41x + -41x Combine like terms: 42x + -41x = 1x 24 + 1x = 33 + 41x + -41x Combine like terms: 41x + -41x = 0 24 + 1x = 33 + 0 24 + 1x = 33 Add '-24' to each side of the equation. 24 + -24 + 1x = 33 + -24 Combine like terms: 24 + -24 = 0 0 + 1x = 33 + -24 1x = 33 + -24 Combine like terms: 33 + -24 = 9 1x = 9 Divide each side by '1'. x = 9 Simplifying x = 9
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