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Simplifying 7(3x + -4) + -3(5x + 3) = 2(x + -3) + 1 Reorder the terms: 7(-4 + 3x) + -3(5x + 3) = 2(x + -3) + 1 (-4 * 7 + 3x * 7) + -3(5x + 3) = 2(x + -3) + 1 (-28 + 21x) + -3(5x + 3) = 2(x + -3) + 1 Reorder the terms: -28 + 21x + -3(3 + 5x) = 2(x + -3) + 1 -28 + 21x + (3 * -3 + 5x * -3) = 2(x + -3) + 1 -28 + 21x + (-9 + -15x) = 2(x + -3) + 1 Reorder the terms: -28 + -9 + 21x + -15x = 2(x + -3) + 1 Combine like terms: -28 + -9 = -37 -37 + 21x + -15x = 2(x + -3) + 1 Combine like terms: 21x + -15x = 6x -37 + 6x = 2(x + -3) + 1 Reorder the terms: -37 + 6x = 2(-3 + x) + 1 -37 + 6x = (-3 * 2 + x * 2) + 1 -37 + 6x = (-6 + 2x) + 1 Reorder the terms: -37 + 6x = -6 + 1 + 2x Combine like terms: -6 + 1 = -5 -37 + 6x = -5 + 2x Solving -37 + 6x = -5 + 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. -37 + 6x + -2x = -5 + 2x + -2x Combine like terms: 6x + -2x = 4x -37 + 4x = -5 + 2x + -2x Combine like terms: 2x + -2x = 0 -37 + 4x = -5 + 0 -37 + 4x = -5 Add '37' to each side of the equation. -37 + 37 + 4x = -5 + 37 Combine like terms: -37 + 37 = 0 0 + 4x = -5 + 37 4x = -5 + 37 Combine like terms: -5 + 37 = 32 4x = 32 Divide each side by '4'. x = 8 Simplifying x = 8
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