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Simplifying 3(2r + 5) + 2(1 + -1x) = 7 + 3x Reorder the terms: 3(5 + 2r) + 2(1 + -1x) = 7 + 3x (5 * 3 + 2r * 3) + 2(1 + -1x) = 7 + 3x (15 + 6r) + 2(1 + -1x) = 7 + 3x 15 + 6r + (1 * 2 + -1x * 2) = 7 + 3x 15 + 6r + (2 + -2x) = 7 + 3x Reorder the terms: 15 + 2 + 6r + -2x = 7 + 3x Combine like terms: 15 + 2 = 17 17 + 6r + -2x = 7 + 3x Solving 17 + 6r + -2x = 7 + 3x Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + 6r + -17 + -2x = 7 + -17 + 3x Reorder the terms: 17 + -17 + 6r + -2x = 7 + -17 + 3x Combine like terms: 17 + -17 = 0 0 + 6r + -2x = 7 + -17 + 3x 6r + -2x = 7 + -17 + 3x Combine like terms: 7 + -17 = -10 6r + -2x = -10 + 3x Add '2x' to each side of the equation. 6r + -2x + 2x = -10 + 3x + 2x Combine like terms: -2x + 2x = 0 6r + 0 = -10 + 3x + 2x 6r = -10 + 3x + 2x Combine like terms: 3x + 2x = 5x 6r = -10 + 5x Divide each side by '6'. r = -1.666666667 + 0.8333333333x Simplifying r = -1.666666667 + 0.8333333333x
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