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Simplifying 4 + -2r = 3(5 + -1r) + 7(r + 1) 4 + -2r = (5 * 3 + -1r * 3) + 7(r + 1) 4 + -2r = (15 + -3r) + 7(r + 1) Reorder the terms: 4 + -2r = 15 + -3r + 7(1 + r) 4 + -2r = 15 + -3r + (1 * 7 + r * 7) 4 + -2r = 15 + -3r + (7 + 7r) Reorder the terms: 4 + -2r = 15 + 7 + -3r + 7r Combine like terms: 15 + 7 = 22 4 + -2r = 22 + -3r + 7r Combine like terms: -3r + 7r = 4r 4 + -2r = 22 + 4r Solving 4 + -2r = 22 + 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. 4 + -2r + -4r = 22 + 4r + -4r Combine like terms: -2r + -4r = -6r 4 + -6r = 22 + 4r + -4r Combine like terms: 4r + -4r = 0 4 + -6r = 22 + 0 4 + -6r = 22 Add '-4' to each side of the equation. 4 + -4 + -6r = 22 + -4 Combine like terms: 4 + -4 = 0 0 + -6r = 22 + -4 -6r = 22 + -4 Combine like terms: 22 + -4 = 18 -6r = 18 Divide each side by '-6'. r = -3 Simplifying r = -3
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