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Simplifying 7(3x + 2) + -5(4x + -3) = 4(x + 2) + 1 Reorder the terms: 7(2 + 3x) + -5(4x + -3) = 4(x + 2) + 1 (2 * 7 + 3x * 7) + -5(4x + -3) = 4(x + 2) + 1 (14 + 21x) + -5(4x + -3) = 4(x + 2) + 1 Reorder the terms: 14 + 21x + -5(-3 + 4x) = 4(x + 2) + 1 14 + 21x + (-3 * -5 + 4x * -5) = 4(x + 2) + 1 14 + 21x + (15 + -20x) = 4(x + 2) + 1 Reorder the terms: 14 + 15 + 21x + -20x = 4(x + 2) + 1 Combine like terms: 14 + 15 = 29 29 + 21x + -20x = 4(x + 2) + 1 Combine like terms: 21x + -20x = 1x 29 + 1x = 4(x + 2) + 1 Reorder the terms: 29 + 1x = 4(2 + x) + 1 29 + 1x = (2 * 4 + x * 4) + 1 29 + 1x = (8 + 4x) + 1 Reorder the terms: 29 + 1x = 8 + 1 + 4x Combine like terms: 8 + 1 = 9 29 + 1x = 9 + 4x Solving 29 + 1x = 9 + 4x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4x' to each side of the equation. 29 + 1x + -4x = 9 + 4x + -4x Combine like terms: 1x + -4x = -3x 29 + -3x = 9 + 4x + -4x Combine like terms: 4x + -4x = 0 29 + -3x = 9 + 0 29 + -3x = 9 Add '-29' to each side of the equation. 29 + -29 + -3x = 9 + -29 Combine like terms: 29 + -29 = 0 0 + -3x = 9 + -29 -3x = 9 + -29 Combine like terms: 9 + -29 = -20 -3x = -20 Divide each side by '-3'. x = 6.666666667 Simplifying x = 6.666666667
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