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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 = -7 29 + 1x = -7 + 4x Solving 29 + 1x = -7 + 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 = -7 + 4x + -4x Combine like terms: 1x + -4x = -3x 29 + -3x = -7 + 4x + -4x Combine like terms: 4x + -4x = 0 29 + -3x = -7 + 0 29 + -3x = -7 Add '-29' to each side of the equation. 29 + -29 + -3x = -7 + -29 Combine like terms: 29 + -29 = 0 0 + -3x = -7 + -29 -3x = -7 + -29 Combine like terms: -7 + -29 = -36 -3x = -36 Divide each side by '-3'. x = 12 Simplifying x = 12
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