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Simplifying 5r + -3r + 12 = 7r + -1r Reorder the terms: 12 + 5r + -3r = 7r + -1r Combine like terms: 5r + -3r = 2r 12 + 2r = 7r + -1r Combine like terms: 7r + -1r = 6r 12 + 2r = 6r Solving 12 + 2r = 6r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-6r' to each side of the equation. 12 + 2r + -6r = 6r + -6r Combine like terms: 2r + -6r = -4r 12 + -4r = 6r + -6r Combine like terms: 6r + -6r = 0 12 + -4r = 0 Add '-12' to each side of the equation. 12 + -12 + -4r = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -4r = 0 + -12 -4r = 0 + -12 Combine like terms: 0 + -12 = -12 -4r = -12 Divide each side by '-4'. r = 3 Simplifying r = 3
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