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Simplifying 9(4x + 1) + 7(x + 4) = 6(4x + 4) + 6(x + -1) Reorder the terms: 9(1 + 4x) + 7(x + 4) = 6(4x + 4) + 6(x + -1) (1 * 9 + 4x * 9) + 7(x + 4) = 6(4x + 4) + 6(x + -1) (9 + 36x) + 7(x + 4) = 6(4x + 4) + 6(x + -1) Reorder the terms: 9 + 36x + 7(4 + x) = 6(4x + 4) + 6(x + -1) 9 + 36x + (4 * 7 + x * 7) = 6(4x + 4) + 6(x + -1) 9 + 36x + (28 + 7x) = 6(4x + 4) + 6(x + -1) Reorder the terms: 9 + 28 + 36x + 7x = 6(4x + 4) + 6(x + -1) Combine like terms: 9 + 28 = 37 37 + 36x + 7x = 6(4x + 4) + 6(x + -1) Combine like terms: 36x + 7x = 43x 37 + 43x = 6(4x + 4) + 6(x + -1) Reorder the terms: 37 + 43x = 6(4 + 4x) + 6(x + -1) 37 + 43x = (4 * 6 + 4x * 6) + 6(x + -1) 37 + 43x = (24 + 24x) + 6(x + -1) Reorder the terms: 37 + 43x = 24 + 24x + 6(-1 + x) 37 + 43x = 24 + 24x + (-1 * 6 + x * 6) 37 + 43x = 24 + 24x + (-6 + 6x) Reorder the terms: 37 + 43x = 24 + -6 + 24x + 6x Combine like terms: 24 + -6 = 18 37 + 43x = 18 + 24x + 6x Combine like terms: 24x + 6x = 30x 37 + 43x = 18 + 30x Solving 37 + 43x = 18 + 30x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-30x' to each side of the equation. 37 + 43x + -30x = 18 + 30x + -30x Combine like terms: 43x + -30x = 13x 37 + 13x = 18 + 30x + -30x Combine like terms: 30x + -30x = 0 37 + 13x = 18 + 0 37 + 13x = 18 Add '-37' to each side of the equation. 37 + -37 + 13x = 18 + -37 Combine like terms: 37 + -37 = 0 0 + 13x = 18 + -37 13x = 18 + -37 Combine like terms: 18 + -37 = -19 13x = -19 Divide each side by '13'. x = -1.461538462 Simplifying x = -1.461538462
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