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Simplifying 6(6 + x + 1) = 7(7 + x + -2) Reorder the terms: 6(6 + 1 + x) = 7(7 + x + -2) Combine like terms: 6 + 1 = 7 6(7 + x) = 7(7 + x + -2) (7 * 6 + x * 6) = 7(7 + x + -2) (42 + 6x) = 7(7 + x + -2) Reorder the terms: 42 + 6x = 7(7 + -2 + x) Combine like terms: 7 + -2 = 5 42 + 6x = 7(5 + x) 42 + 6x = (5 * 7 + x * 7) 42 + 6x = (35 + 7x) Solving 42 + 6x = 35 + 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. 42 + 6x + -7x = 35 + 7x + -7x Combine like terms: 6x + -7x = -1x 42 + -1x = 35 + 7x + -7x Combine like terms: 7x + -7x = 0 42 + -1x = 35 + 0 42 + -1x = 35 Add '-42' to each side of the equation. 42 + -42 + -1x = 35 + -42 Combine like terms: 42 + -42 = 0 0 + -1x = 35 + -42 -1x = 35 + -42 Combine like terms: 35 + -42 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7
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