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Simplifying 7(3r + -1) + -1(r + 5) = -52 Reorder the terms: 7(-1 + 3r) + -1(r + 5) = -52 (-1 * 7 + 3r * 7) + -1(r + 5) = -52 (-7 + 21r) + -1(r + 5) = -52 Reorder the terms: -7 + 21r + -1(5 + r) = -52 -7 + 21r + (5 * -1 + r * -1) = -52 -7 + 21r + (-5 + -1r) = -52 Reorder the terms: -7 + -5 + 21r + -1r = -52 Combine like terms: -7 + -5 = -12 -12 + 21r + -1r = -52 Combine like terms: 21r + -1r = 20r -12 + 20r = -52 Solving -12 + 20r = -52 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + 20r = -52 + 12 Combine like terms: -12 + 12 = 0 0 + 20r = -52 + 12 20r = -52 + 12 Combine like terms: -52 + 12 = -40 20r = -40 Divide each side by '20'. r = -2 Simplifying r = -2
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