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Simplifying 20(x + 10) + 60(x + 2) = 10(6x + -18) + 26(5x + 1) Reorder the terms: 20(10 + x) + 60(x + 2) = 10(6x + -18) + 26(5x + 1) (10 * 20 + x * 20) + 60(x + 2) = 10(6x + -18) + 26(5x + 1) (200 + 20x) + 60(x + 2) = 10(6x + -18) + 26(5x + 1) Reorder the terms: 200 + 20x + 60(2 + x) = 10(6x + -18) + 26(5x + 1) 200 + 20x + (2 * 60 + x * 60) = 10(6x + -18) + 26(5x + 1) 200 + 20x + (120 + 60x) = 10(6x + -18) + 26(5x + 1) Reorder the terms: 200 + 120 + 20x + 60x = 10(6x + -18) + 26(5x + 1) Combine like terms: 200 + 120 = 320 320 + 20x + 60x = 10(6x + -18) + 26(5x + 1) Combine like terms: 20x + 60x = 80x 320 + 80x = 10(6x + -18) + 26(5x + 1) Reorder the terms: 320 + 80x = 10(-18 + 6x) + 26(5x + 1) 320 + 80x = (-18 * 10 + 6x * 10) + 26(5x + 1) 320 + 80x = (-180 + 60x) + 26(5x + 1) Reorder the terms: 320 + 80x = -180 + 60x + 26(1 + 5x) 320 + 80x = -180 + 60x + (1 * 26 + 5x * 26) 320 + 80x = -180 + 60x + (26 + 130x) Reorder the terms: 320 + 80x = -180 + 26 + 60x + 130x Combine like terms: -180 + 26 = -154 320 + 80x = -154 + 60x + 130x Combine like terms: 60x + 130x = 190x 320 + 80x = -154 + 190x Solving 320 + 80x = -154 + 190x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-190x' to each side of the equation. 320 + 80x + -190x = -154 + 190x + -190x Combine like terms: 80x + -190x = -110x 320 + -110x = -154 + 190x + -190x Combine like terms: 190x + -190x = 0 320 + -110x = -154 + 0 320 + -110x = -154 Add '-320' to each side of the equation. 320 + -320 + -110x = -154 + -320 Combine like terms: 320 + -320 = 0 0 + -110x = -154 + -320 -110x = -154 + -320 Combine like terms: -154 + -320 = -474 -110x = -474 Divide each side by '-110'. x = 4.309090909 Simplifying x = 4.309090909
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