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Simplifying 6(6x + -5) + -5(7x + -8) = 12(4 + -1x) + 1 Reorder the terms: 6(-5 + 6x) + -5(7x + -8) = 12(4 + -1x) + 1 (-5 * 6 + 6x * 6) + -5(7x + -8) = 12(4 + -1x) + 1 (-30 + 36x) + -5(7x + -8) = 12(4 + -1x) + 1 Reorder the terms: -30 + 36x + -5(-8 + 7x) = 12(4 + -1x) + 1 -30 + 36x + (-8 * -5 + 7x * -5) = 12(4 + -1x) + 1 -30 + 36x + (40 + -35x) = 12(4 + -1x) + 1 Reorder the terms: -30 + 40 + 36x + -35x = 12(4 + -1x) + 1 Combine like terms: -30 + 40 = 10 10 + 36x + -35x = 12(4 + -1x) + 1 Combine like terms: 36x + -35x = 1x 10 + 1x = 12(4 + -1x) + 1 10 + 1x = (4 * 12 + -1x * 12) + 1 10 + 1x = (48 + -12x) + 1 Reorder the terms: 10 + 1x = 48 + 1 + -12x Combine like terms: 48 + 1 = 49 10 + 1x = 49 + -12x Solving 10 + 1x = 49 + -12x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12x' to each side of the equation. 10 + 1x + 12x = 49 + -12x + 12x Combine like terms: 1x + 12x = 13x 10 + 13x = 49 + -12x + 12x Combine like terms: -12x + 12x = 0 10 + 13x = 49 + 0 10 + 13x = 49 Add '-10' to each side of the equation. 10 + -10 + 13x = 49 + -10 Combine like terms: 10 + -10 = 0 0 + 13x = 49 + -10 13x = 49 + -10 Combine like terms: 49 + -10 = 39 13x = 39 Divide each side by '13'. x = 3 Simplifying x = 3
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