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Simplifying 5(2x + -2) + 2(x + 6) = 5(x + 7) + -1(x + 3) Reorder the terms: 5(-2 + 2x) + 2(x + 6) = 5(x + 7) + -1(x + 3) (-2 * 5 + 2x * 5) + 2(x + 6) = 5(x + 7) + -1(x + 3) (-10 + 10x) + 2(x + 6) = 5(x + 7) + -1(x + 3) Reorder the terms: -10 + 10x + 2(6 + x) = 5(x + 7) + -1(x + 3) -10 + 10x + (6 * 2 + x * 2) = 5(x + 7) + -1(x + 3) -10 + 10x + (12 + 2x) = 5(x + 7) + -1(x + 3) Reorder the terms: -10 + 12 + 10x + 2x = 5(x + 7) + -1(x + 3) Combine like terms: -10 + 12 = 2 2 + 10x + 2x = 5(x + 7) + -1(x + 3) Combine like terms: 10x + 2x = 12x 2 + 12x = 5(x + 7) + -1(x + 3) Reorder the terms: 2 + 12x = 5(7 + x) + -1(x + 3) 2 + 12x = (7 * 5 + x * 5) + -1(x + 3) 2 + 12x = (35 + 5x) + -1(x + 3) Reorder the terms: 2 + 12x = 35 + 5x + -1(3 + x) 2 + 12x = 35 + 5x + (3 * -1 + x * -1) 2 + 12x = 35 + 5x + (-3 + -1x) Reorder the terms: 2 + 12x = 35 + -3 + 5x + -1x Combine like terms: 35 + -3 = 32 2 + 12x = 32 + 5x + -1x Combine like terms: 5x + -1x = 4x 2 + 12x = 32 + 4x Solving 2 + 12x = 32 + 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. 2 + 12x + -4x = 32 + 4x + -4x Combine like terms: 12x + -4x = 8x 2 + 8x = 32 + 4x + -4x Combine like terms: 4x + -4x = 0 2 + 8x = 32 + 0 2 + 8x = 32 Add '-2' to each side of the equation. 2 + -2 + 8x = 32 + -2 Combine like terms: 2 + -2 = 0 0 + 8x = 32 + -2 8x = 32 + -2 Combine like terms: 32 + -2 = 30 8x = 30 Divide each side by '8'. x = 3.75 Simplifying x = 3.75
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