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Simplifying 3(2x + -2) + -1r + 3x = 2(7x + 1) + -5x + -9 Reorder the terms: 3(-2 + 2x) + -1r + 3x = 2(7x + 1) + -5x + -9 (-2 * 3 + 2x * 3) + -1r + 3x = 2(7x + 1) + -5x + -9 (-6 + 6x) + -1r + 3x = 2(7x + 1) + -5x + -9 Reorder the terms: -6 + -1r + 6x + 3x = 2(7x + 1) + -5x + -9 Combine like terms: 6x + 3x = 9x -6 + -1r + 9x = 2(7x + 1) + -5x + -9 Reorder the terms: -6 + -1r + 9x = 2(1 + 7x) + -5x + -9 -6 + -1r + 9x = (1 * 2 + 7x * 2) + -5x + -9 -6 + -1r + 9x = (2 + 14x) + -5x + -9 Reorder the terms: -6 + -1r + 9x = 2 + -9 + 14x + -5x Combine like terms: 2 + -9 = -7 -6 + -1r + 9x = -7 + 14x + -5x Combine like terms: 14x + -5x = 9x -6 + -1r + 9x = -7 + 9x Add '-9x' to each side of the equation. -6 + -1r + 9x + -9x = -7 + 9x + -9x Combine like terms: 9x + -9x = 0 -6 + -1r + 0 = -7 + 9x + -9x -6 + -1r = -7 + 9x + -9x Combine like terms: 9x + -9x = 0 -6 + -1r = -7 + 0 -6 + -1r = -7 Solving -6 + -1r = -7 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1r = -7 + 6 Combine like terms: -6 + 6 = 0 0 + -1r = -7 + 6 -1r = -7 + 6 Combine like terms: -7 + 6 = -1 -1r = -1 Divide each side by '-1'. r = 1 Simplifying r = 1
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