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Simplifying -1(7 + 5r) + 2(1 + 6r) = -47 (7 * -1 + 5r * -1) + 2(1 + 6r) = -47 (-7 + -5r) + 2(1 + 6r) = -47 -7 + -5r + (1 * 2 + 6r * 2) = -47 -7 + -5r + (2 + 12r) = -47 Reorder the terms: -7 + 2 + -5r + 12r = -47 Combine like terms: -7 + 2 = -5 -5 + -5r + 12r = -47 Combine like terms: -5r + 12r = 7r -5 + 7r = -47 Solving -5 + 7r = -47 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + 7r = -47 + 5 Combine like terms: -5 + 5 = 0 0 + 7r = -47 + 5 7r = -47 + 5 Combine like terms: -47 + 5 = -42 7r = -42 Divide each side by '7'. r = -6 Simplifying r = -6
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