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Simplifying 5(x + -7) + -2(3x + 4) = 7(2x + 1) + -9(x + -6) Reorder the terms: 5(-7 + x) + -2(3x + 4) = 7(2x + 1) + -9(x + -6) (-7 * 5 + x * 5) + -2(3x + 4) = 7(2x + 1) + -9(x + -6) (-35 + 5x) + -2(3x + 4) = 7(2x + 1) + -9(x + -6) Reorder the terms: -35 + 5x + -2(4 + 3x) = 7(2x + 1) + -9(x + -6) -35 + 5x + (4 * -2 + 3x * -2) = 7(2x + 1) + -9(x + -6) -35 + 5x + (-8 + -6x) = 7(2x + 1) + -9(x + -6) Reorder the terms: -35 + -8 + 5x + -6x = 7(2x + 1) + -9(x + -6) Combine like terms: -35 + -8 = -43 -43 + 5x + -6x = 7(2x + 1) + -9(x + -6) Combine like terms: 5x + -6x = -1x -43 + -1x = 7(2x + 1) + -9(x + -6) Reorder the terms: -43 + -1x = 7(1 + 2x) + -9(x + -6) -43 + -1x = (1 * 7 + 2x * 7) + -9(x + -6) -43 + -1x = (7 + 14x) + -9(x + -6) Reorder the terms: -43 + -1x = 7 + 14x + -9(-6 + x) -43 + -1x = 7 + 14x + (-6 * -9 + x * -9) -43 + -1x = 7 + 14x + (54 + -9x) Reorder the terms: -43 + -1x = 7 + 54 + 14x + -9x Combine like terms: 7 + 54 = 61 -43 + -1x = 61 + 14x + -9x Combine like terms: 14x + -9x = 5x -43 + -1x = 61 + 5x Solving -43 + -1x = 61 + 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. -43 + -1x + -5x = 61 + 5x + -5x Combine like terms: -1x + -5x = -6x -43 + -6x = 61 + 5x + -5x Combine like terms: 5x + -5x = 0 -43 + -6x = 61 + 0 -43 + -6x = 61 Add '43' to each side of the equation. -43 + 43 + -6x = 61 + 43 Combine like terms: -43 + 43 = 0 0 + -6x = 61 + 43 -6x = 61 + 43 Combine like terms: 61 + 43 = 104 -6x = 104 Divide each side by '-6'. x = -17.33333333 Simplifying x = -17.33333333
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