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Simplifying 4r + 7 + -6r + 1 = 7r + 9 + -3r + -7 Reorder the terms: 7 + 1 + 4r + -6r = 7r + 9 + -3r + -7 Combine like terms: 7 + 1 = 8 8 + 4r + -6r = 7r + 9 + -3r + -7 Combine like terms: 4r + -6r = -2r 8 + -2r = 7r + 9 + -3r + -7 Reorder the terms: 8 + -2r = 9 + -7 + 7r + -3r Combine like terms: 9 + -7 = 2 8 + -2r = 2 + 7r + -3r Combine like terms: 7r + -3r = 4r 8 + -2r = 2 + 4r Solving 8 + -2r = 2 + 4r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-4r' to each side of the equation. 8 + -2r + -4r = 2 + 4r + -4r Combine like terms: -2r + -4r = -6r 8 + -6r = 2 + 4r + -4r Combine like terms: 4r + -4r = 0 8 + -6r = 2 + 0 8 + -6r = 2 Add '-8' to each side of the equation. 8 + -8 + -6r = 2 + -8 Combine like terms: 8 + -8 = 0 0 + -6r = 2 + -8 -6r = 2 + -8 Combine like terms: 2 + -8 = -6 -6r = -6 Divide each side by '-6'. r = 1 Simplifying r = 1
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