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Simplifying 1(2x + -2) + 7(x + -8) = 1(2x + 16) + 5(x + 16) Reorder the terms: 1(-2 + 2x) + 7(x + -8) = 1(2x + 16) + 5(x + 16) (-2 * 1 + 2x * 1) + 7(x + -8) = 1(2x + 16) + 5(x + 16) (-2 + 2x) + 7(x + -8) = 1(2x + 16) + 5(x + 16) Reorder the terms: -2 + 2x + 7(-8 + x) = 1(2x + 16) + 5(x + 16) -2 + 2x + (-8 * 7 + x * 7) = 1(2x + 16) + 5(x + 16) -2 + 2x + (-56 + 7x) = 1(2x + 16) + 5(x + 16) Reorder the terms: -2 + -56 + 2x + 7x = 1(2x + 16) + 5(x + 16) Combine like terms: -2 + -56 = -58 -58 + 2x + 7x = 1(2x + 16) + 5(x + 16) Combine like terms: 2x + 7x = 9x -58 + 9x = 1(2x + 16) + 5(x + 16) Reorder the terms: -58 + 9x = 1(16 + 2x) + 5(x + 16) -58 + 9x = (16 * 1 + 2x * 1) + 5(x + 16) -58 + 9x = (16 + 2x) + 5(x + 16) Reorder the terms: -58 + 9x = 16 + 2x + 5(16 + x) -58 + 9x = 16 + 2x + (16 * 5 + x * 5) -58 + 9x = 16 + 2x + (80 + 5x) Reorder the terms: -58 + 9x = 16 + 80 + 2x + 5x Combine like terms: 16 + 80 = 96 -58 + 9x = 96 + 2x + 5x Combine like terms: 2x + 5x = 7x -58 + 9x = 96 + 7x Solving -58 + 9x = 96 + 7x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7x' to each side of the equation. -58 + 9x + -7x = 96 + 7x + -7x Combine like terms: 9x + -7x = 2x -58 + 2x = 96 + 7x + -7x Combine like terms: 7x + -7x = 0 -58 + 2x = 96 + 0 -58 + 2x = 96 Add '58' to each side of the equation. -58 + 58 + 2x = 96 + 58 Combine like terms: -58 + 58 = 0 0 + 2x = 96 + 58 2x = 96 + 58 Combine like terms: 96 + 58 = 154 2x = 154 Divide each side by '2'. x = 77 Simplifying x = 77
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