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Simplifying 7(4x + -11) + -5(1 + 2x) = 41 + 3(2x + 7) Reorder the terms: 7(-11 + 4x) + -5(1 + 2x) = 41 + 3(2x + 7) (-11 * 7 + 4x * 7) + -5(1 + 2x) = 41 + 3(2x + 7) (-77 + 28x) + -5(1 + 2x) = 41 + 3(2x + 7) -77 + 28x + (1 * -5 + 2x * -5) = 41 + 3(2x + 7) -77 + 28x + (-5 + -10x) = 41 + 3(2x + 7) Reorder the terms: -77 + -5 + 28x + -10x = 41 + 3(2x + 7) Combine like terms: -77 + -5 = -82 -82 + 28x + -10x = 41 + 3(2x + 7) Combine like terms: 28x + -10x = 18x -82 + 18x = 41 + 3(2x + 7) Reorder the terms: -82 + 18x = 41 + 3(7 + 2x) -82 + 18x = 41 + (7 * 3 + 2x * 3) -82 + 18x = 41 + (21 + 6x) Combine like terms: 41 + 21 = 62 -82 + 18x = 62 + 6x Solving -82 + 18x = 62 + 6x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6x' to each side of the equation. -82 + 18x + -6x = 62 + 6x + -6x Combine like terms: 18x + -6x = 12x -82 + 12x = 62 + 6x + -6x Combine like terms: 6x + -6x = 0 -82 + 12x = 62 + 0 -82 + 12x = 62 Add '82' to each side of the equation. -82 + 82 + 12x = 62 + 82 Combine like terms: -82 + 82 = 0 0 + 12x = 62 + 82 12x = 62 + 82 Combine like terms: 62 + 82 = 144 12x = 144 Divide each side by '12'. x = 12 Simplifying x = 12
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