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Simplifying 15(x + 7) + -1(7x + 4) = 1 + (7x + 6) Reorder the terms: 15(7 + x) + -1(7x + 4) = 1 + (7x + 6) (7 * 15 + x * 15) + -1(7x + 4) = 1 + (7x + 6) (105 + 15x) + -1(7x + 4) = 1 + (7x + 6) Reorder the terms: 105 + 15x + -1(4 + 7x) = 1 + (7x + 6) 105 + 15x + (4 * -1 + 7x * -1) = 1 + (7x + 6) 105 + 15x + (-4 + -7x) = 1 + (7x + 6) Reorder the terms: 105 + -4 + 15x + -7x = 1 + (7x + 6) Combine like terms: 105 + -4 = 101 101 + 15x + -7x = 1 + (7x + 6) Combine like terms: 15x + -7x = 8x 101 + 8x = 1 + (7x + 6) Reorder the terms: 101 + 8x = 1 + (6 + 7x) Remove parenthesis around (6 + 7x) 101 + 8x = 1 + 6 + 7x Combine like terms: 1 + 6 = 7 101 + 8x = 7 + 7x Solving 101 + 8x = 7 + 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. 101 + 8x + -7x = 7 + 7x + -7x Combine like terms: 8x + -7x = 1x 101 + 1x = 7 + 7x + -7x Combine like terms: 7x + -7x = 0 101 + 1x = 7 + 0 101 + 1x = 7 Add '-101' to each side of the equation. 101 + -101 + 1x = 7 + -101 Combine like terms: 101 + -101 = 0 0 + 1x = 7 + -101 1x = 7 + -101 Combine like terms: 7 + -101 = -94 1x = -94 Divide each side by '1'. x = -94 Simplifying x = -94
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