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Simplifying 3(5x + -5) + 7(x + 3) = 4(x + 8) + -1(x + 2) Reorder the terms: 3(-5 + 5x) + 7(x + 3) = 4(x + 8) + -1(x + 2) (-5 * 3 + 5x * 3) + 7(x + 3) = 4(x + 8) + -1(x + 2) (-15 + 15x) + 7(x + 3) = 4(x + 8) + -1(x + 2) Reorder the terms: -15 + 15x + 7(3 + x) = 4(x + 8) + -1(x + 2) -15 + 15x + (3 * 7 + x * 7) = 4(x + 8) + -1(x + 2) -15 + 15x + (21 + 7x) = 4(x + 8) + -1(x + 2) Reorder the terms: -15 + 21 + 15x + 7x = 4(x + 8) + -1(x + 2) Combine like terms: -15 + 21 = 6 6 + 15x + 7x = 4(x + 8) + -1(x + 2) Combine like terms: 15x + 7x = 22x 6 + 22x = 4(x + 8) + -1(x + 2) Reorder the terms: 6 + 22x = 4(8 + x) + -1(x + 2) 6 + 22x = (8 * 4 + x * 4) + -1(x + 2) 6 + 22x = (32 + 4x) + -1(x + 2) Reorder the terms: 6 + 22x = 32 + 4x + -1(2 + x) 6 + 22x = 32 + 4x + (2 * -1 + x * -1) 6 + 22x = 32 + 4x + (-2 + -1x) Reorder the terms: 6 + 22x = 32 + -2 + 4x + -1x Combine like terms: 32 + -2 = 30 6 + 22x = 30 + 4x + -1x Combine like terms: 4x + -1x = 3x 6 + 22x = 30 + 3x Solving 6 + 22x = 30 + 3x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3x' to each side of the equation. 6 + 22x + -3x = 30 + 3x + -3x Combine like terms: 22x + -3x = 19x 6 + 19x = 30 + 3x + -3x Combine like terms: 3x + -3x = 0 6 + 19x = 30 + 0 6 + 19x = 30 Add '-6' to each side of the equation. 6 + -6 + 19x = 30 + -6 Combine like terms: 6 + -6 = 0 0 + 19x = 30 + -6 19x = 30 + -6 Combine like terms: 30 + -6 = 24 19x = 24 Divide each side by '19'. x = 1.263157895 Simplifying x = 1.263157895
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