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Simplifying 5(6x + -3) + 6(x + 7) = 6(x + 9) + -1(x + 7) Reorder the terms: 5(-3 + 6x) + 6(x + 7) = 6(x + 9) + -1(x + 7) (-3 * 5 + 6x * 5) + 6(x + 7) = 6(x + 9) + -1(x + 7) (-15 + 30x) + 6(x + 7) = 6(x + 9) + -1(x + 7) Reorder the terms: -15 + 30x + 6(7 + x) = 6(x + 9) + -1(x + 7) -15 + 30x + (7 * 6 + x * 6) = 6(x + 9) + -1(x + 7) -15 + 30x + (42 + 6x) = 6(x + 9) + -1(x + 7) Reorder the terms: -15 + 42 + 30x + 6x = 6(x + 9) + -1(x + 7) Combine like terms: -15 + 42 = 27 27 + 30x + 6x = 6(x + 9) + -1(x + 7) Combine like terms: 30x + 6x = 36x 27 + 36x = 6(x + 9) + -1(x + 7) Reorder the terms: 27 + 36x = 6(9 + x) + -1(x + 7) 27 + 36x = (9 * 6 + x * 6) + -1(x + 7) 27 + 36x = (54 + 6x) + -1(x + 7) Reorder the terms: 27 + 36x = 54 + 6x + -1(7 + x) 27 + 36x = 54 + 6x + (7 * -1 + x * -1) 27 + 36x = 54 + 6x + (-7 + -1x) Reorder the terms: 27 + 36x = 54 + -7 + 6x + -1x Combine like terms: 54 + -7 = 47 27 + 36x = 47 + 6x + -1x Combine like terms: 6x + -1x = 5x 27 + 36x = 47 + 5x Solving 27 + 36x = 47 + 5x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5x' to each side of the equation. 27 + 36x + -5x = 47 + 5x + -5x Combine like terms: 36x + -5x = 31x 27 + 31x = 47 + 5x + -5x Combine like terms: 5x + -5x = 0 27 + 31x = 47 + 0 27 + 31x = 47 Add '-27' to each side of the equation. 27 + -27 + 31x = 47 + -27 Combine like terms: 27 + -27 = 0 0 + 31x = 47 + -27 31x = 47 + -27 Combine like terms: 47 + -27 = 20 31x = 20 Divide each side by '31'. x = 0.6451612903 Simplifying x = 0.6451612903
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