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Simplifying (2x + -3)(x + 7) = (x + 4)(2x + -3) + 3 Reorder the terms: (-3 + 2x)(x + 7) = (x + 4)(2x + -3) + 3 Reorder the terms: (-3 + 2x)(7 + x) = (x + 4)(2x + -3) + 3 Multiply (-3 + 2x) * (7 + x) (-3(7 + x) + 2x * (7 + x)) = (x + 4)(2x + -3) + 3 ((7 * -3 + x * -3) + 2x * (7 + x)) = (x + 4)(2x + -3) + 3 ((-21 + -3x) + 2x * (7 + x)) = (x + 4)(2x + -3) + 3 (-21 + -3x + (7 * 2x + x * 2x)) = (x + 4)(2x + -3) + 3 (-21 + -3x + (14x + 2x2)) = (x + 4)(2x + -3) + 3 Combine like terms: -3x + 14x = 11x (-21 + 11x + 2x2) = (x + 4)(2x + -3) + 3 Reorder the terms: -21 + 11x + 2x2 = (4 + x)(2x + -3) + 3 Reorder the terms: -21 + 11x + 2x2 = (4 + x)(-3 + 2x) + 3 Multiply (4 + x) * (-3 + 2x) -21 + 11x + 2x2 = (4(-3 + 2x) + x(-3 + 2x)) + 3 -21 + 11x + 2x2 = ((-3 * 4 + 2x * 4) + x(-3 + 2x)) + 3 -21 + 11x + 2x2 = ((-12 + 8x) + x(-3 + 2x)) + 3 -21 + 11x + 2x2 = (-12 + 8x + (-3 * x + 2x * x)) + 3 -21 + 11x + 2x2 = (-12 + 8x + (-3x + 2x2)) + 3 Combine like terms: 8x + -3x = 5x -21 + 11x + 2x2 = (-12 + 5x + 2x2) + 3 Reorder the terms: -21 + 11x + 2x2 = -12 + 3 + 5x + 2x2 Combine like terms: -12 + 3 = -9 -21 + 11x + 2x2 = -9 + 5x + 2x2 Add '-2x2' to each side of the equation. -21 + 11x + 2x2 + -2x2 = -9 + 5x + 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -21 + 11x + 0 = -9 + 5x + 2x2 + -2x2 -21 + 11x = -9 + 5x + 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -21 + 11x = -9 + 5x + 0 -21 + 11x = -9 + 5x Solving -21 + 11x = -9 + 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. -21 + 11x + -5x = -9 + 5x + -5x Combine like terms: 11x + -5x = 6x -21 + 6x = -9 + 5x + -5x Combine like terms: 5x + -5x = 0 -21 + 6x = -9 + 0 -21 + 6x = -9 Add '21' to each side of the equation. -21 + 21 + 6x = -9 + 21 Combine like terms: -21 + 21 = 0 0 + 6x = -9 + 21 6x = -9 + 21 Combine like terms: -9 + 21 = 12 6x = 12 Divide each side by '6'. x = 2 Simplifying x = 2
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