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Simplifying (7t + -2) + -1(-3r + 1) = -3(1 + -3t) Reorder the terms: (-2 + 7t) + -1(-3r + 1) = -3(1 + -3t) Remove parenthesis around (-2 + 7t) -2 + 7t + -1(-3r + 1) = -3(1 + -3t) Reorder the terms: -2 + 7t + -1(1 + -3r) = -3(1 + -3t) -2 + 7t + (1 * -1 + -3r * -1) = -3(1 + -3t) -2 + 7t + (-1 + 3r) = -3(1 + -3t) Reorder the terms: -2 + -1 + 3r + 7t = -3(1 + -3t) Combine like terms: -2 + -1 = -3 -3 + 3r + 7t = -3(1 + -3t) -3 + 3r + 7t = (1 * -3 + -3t * -3) -3 + 3r + 7t = (-3 + 9t) Add '3' to each side of the equation. -3 + 3r + 3 + 7t = -3 + 3 + 9t Reorder the terms: -3 + 3 + 3r + 7t = -3 + 3 + 9t Combine like terms: -3 + 3 = 0 0 + 3r + 7t = -3 + 3 + 9t 3r + 7t = -3 + 3 + 9t Combine like terms: -3 + 3 = 0 3r + 7t = 0 + 9t 3r + 7t = 9t Solving 3r + 7t = 9t Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-7t' to each side of the equation. 3r + 7t + -7t = 9t + -7t Combine like terms: 7t + -7t = 0 3r + 0 = 9t + -7t 3r = 9t + -7t Combine like terms: 9t + -7t = 2t 3r = 2t Divide each side by '3'. r = 0.6666666667t Simplifying r = 0.6666666667t
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