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