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Simplifying 7x + -3[7(x + 3) + -5(x + 4)] = 5(x + 1) Reorder the terms: 7x + -3[7(3 + x) + -5(x + 4)] = 5(x + 1) 7x + -3[(3 * 7 + x * 7) + -5(x + 4)] = 5(x + 1) 7x + -3[(21 + 7x) + -5(x + 4)] = 5(x + 1) Reorder the terms: 7x + -3[21 + 7x + -5(4 + x)] = 5(x + 1) 7x + -3[21 + 7x + (4 * -5 + x * -5)] = 5(x + 1) 7x + -3[21 + 7x + (-20 + -5x)] = 5(x + 1) Reorder the terms: 7x + -3[21 + -20 + 7x + -5x] = 5(x + 1) Combine like terms: 21 + -20 = 1 7x + -3[1 + 7x + -5x] = 5(x + 1) Combine like terms: 7x + -5x = 2x 7x + -3[1 + 2x] = 5(x + 1) 7x + [1 * -3 + 2x * -3] = 5(x + 1) 7x + [-3 + -6x] = 5(x + 1) Reorder the terms: -3 + 7x + -6x = 5(x + 1) Combine like terms: 7x + -6x = 1x -3 + 1x = 5(x + 1) Reorder the terms: -3 + 1x = 5(1 + x) -3 + 1x = (1 * 5 + x * 5) -3 + 1x = (5 + 5x) Solving -3 + 1x = 5 + 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. -3 + 1x + -5x = 5 + 5x + -5x Combine like terms: 1x + -5x = -4x -3 + -4x = 5 + 5x + -5x Combine like terms: 5x + -5x = 0 -3 + -4x = 5 + 0 -3 + -4x = 5 Add '3' to each side of the equation. -3 + 3 + -4x = 5 + 3 Combine like terms: -3 + 3 = 0 0 + -4x = 5 + 3 -4x = 5 + 3 Combine like terms: 5 + 3 = 8 -4x = 8 Divide each side by '-4'. x = -2 Simplifying x = -2
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