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Simplifying 4(6x + -7) + 3(x + 5) = 7(x + 9) + -1(x + 8) Reorder the terms: 4(-7 + 6x) + 3(x + 5) = 7(x + 9) + -1(x + 8) (-7 * 4 + 6x * 4) + 3(x + 5) = 7(x + 9) + -1(x + 8) (-28 + 24x) + 3(x + 5) = 7(x + 9) + -1(x + 8) Reorder the terms: -28 + 24x + 3(5 + x) = 7(x + 9) + -1(x + 8) -28 + 24x + (5 * 3 + x * 3) = 7(x + 9) + -1(x + 8) -28 + 24x + (15 + 3x) = 7(x + 9) + -1(x + 8) Reorder the terms: -28 + 15 + 24x + 3x = 7(x + 9) + -1(x + 8) Combine like terms: -28 + 15 = -13 -13 + 24x + 3x = 7(x + 9) + -1(x + 8) Combine like terms: 24x + 3x = 27x -13 + 27x = 7(x + 9) + -1(x + 8) Reorder the terms: -13 + 27x = 7(9 + x) + -1(x + 8) -13 + 27x = (9 * 7 + x * 7) + -1(x + 8) -13 + 27x = (63 + 7x) + -1(x + 8) Reorder the terms: -13 + 27x = 63 + 7x + -1(8 + x) -13 + 27x = 63 + 7x + (8 * -1 + x * -1) -13 + 27x = 63 + 7x + (-8 + -1x) Reorder the terms: -13 + 27x = 63 + -8 + 7x + -1x Combine like terms: 63 + -8 = 55 -13 + 27x = 55 + 7x + -1x Combine like terms: 7x + -1x = 6x -13 + 27x = 55 + 6x Solving -13 + 27x = 55 + 6x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6x' to each side of the equation. -13 + 27x + -6x = 55 + 6x + -6x Combine like terms: 27x + -6x = 21x -13 + 21x = 55 + 6x + -6x Combine like terms: 6x + -6x = 0 -13 + 21x = 55 + 0 -13 + 21x = 55 Add '13' to each side of the equation. -13 + 13 + 21x = 55 + 13 Combine like terms: -13 + 13 = 0 0 + 21x = 55 + 13 21x = 55 + 13 Combine like terms: 55 + 13 = 68 21x = 68 Divide each side by '21'. x = 3.238095238 Simplifying x = 3.238095238
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