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Simplifying 19 + -6r + 1 = -7(-6r + 19) + 3r Reorder the terms: 19 + 1 + -6r = -7(-6r + 19) + 3r Combine like terms: 19 + 1 = 20 20 + -6r = -7(-6r + 19) + 3r Reorder the terms: 20 + -6r = -7(19 + -6r) + 3r 20 + -6r = (19 * -7 + -6r * -7) + 3r 20 + -6r = (-133 + 42r) + 3r Combine like terms: 42r + 3r = 45r 20 + -6r = -133 + 45r Solving 20 + -6r = -133 + 45r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-45r' to each side of the equation. 20 + -6r + -45r = -133 + 45r + -45r Combine like terms: -6r + -45r = -51r 20 + -51r = -133 + 45r + -45r Combine like terms: 45r + -45r = 0 20 + -51r = -133 + 0 20 + -51r = -133 Add '-20' to each side of the equation. 20 + -20 + -51r = -133 + -20 Combine like terms: 20 + -20 = 0 0 + -51r = -133 + -20 -51r = -133 + -20 Combine like terms: -133 + -20 = -153 -51r = -153 Divide each side by '-51'. r = 3 Simplifying r = 3
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