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Simplifying 6(x + 1) + -4(2x + 3) = 7(x + -1) + 5(9 + -1x) Reorder the terms: 6(1 + x) + -4(2x + 3) = 7(x + -1) + 5(9 + -1x) (1 * 6 + x * 6) + -4(2x + 3) = 7(x + -1) + 5(9 + -1x) (6 + 6x) + -4(2x + 3) = 7(x + -1) + 5(9 + -1x) Reorder the terms: 6 + 6x + -4(3 + 2x) = 7(x + -1) + 5(9 + -1x) 6 + 6x + (3 * -4 + 2x * -4) = 7(x + -1) + 5(9 + -1x) 6 + 6x + (-12 + -8x) = 7(x + -1) + 5(9 + -1x) Reorder the terms: 6 + -12 + 6x + -8x = 7(x + -1) + 5(9 + -1x) Combine like terms: 6 + -12 = -6 -6 + 6x + -8x = 7(x + -1) + 5(9 + -1x) Combine like terms: 6x + -8x = -2x -6 + -2x = 7(x + -1) + 5(9 + -1x) Reorder the terms: -6 + -2x = 7(-1 + x) + 5(9 + -1x) -6 + -2x = (-1 * 7 + x * 7) + 5(9 + -1x) -6 + -2x = (-7 + 7x) + 5(9 + -1x) -6 + -2x = -7 + 7x + (9 * 5 + -1x * 5) -6 + -2x = -7 + 7x + (45 + -5x) Reorder the terms: -6 + -2x = -7 + 45 + 7x + -5x Combine like terms: -7 + 45 = 38 -6 + -2x = 38 + 7x + -5x Combine like terms: 7x + -5x = 2x -6 + -2x = 38 + 2x Solving -6 + -2x = 38 + 2x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2x' to each side of the equation. -6 + -2x + -2x = 38 + 2x + -2x Combine like terms: -2x + -2x = -4x -6 + -4x = 38 + 2x + -2x Combine like terms: 2x + -2x = 0 -6 + -4x = 38 + 0 -6 + -4x = 38 Add '6' to each side of the equation. -6 + 6 + -4x = 38 + 6 Combine like terms: -6 + 6 = 0 0 + -4x = 38 + 6 -4x = 38 + 6 Combine like terms: 38 + 6 = 44 -4x = 44 Divide each side by '-4'. x = -11 Simplifying x = -11
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