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Simplifying r + -3 + r + 4 = 3(r + 5) + -5(r + -10) Reorder the terms: -3 + 4 + r + r = 3(r + 5) + -5(r + -10) Combine like terms: -3 + 4 = 1 1 + r + r = 3(r + 5) + -5(r + -10) Combine like terms: r + r = 2r 1 + 2r = 3(r + 5) + -5(r + -10) Reorder the terms: 1 + 2r = 3(5 + r) + -5(r + -10) 1 + 2r = (5 * 3 + r * 3) + -5(r + -10) 1 + 2r = (15 + 3r) + -5(r + -10) Reorder the terms: 1 + 2r = 15 + 3r + -5(-10 + r) 1 + 2r = 15 + 3r + (-10 * -5 + r * -5) 1 + 2r = 15 + 3r + (50 + -5r) Reorder the terms: 1 + 2r = 15 + 50 + 3r + -5r Combine like terms: 15 + 50 = 65 1 + 2r = 65 + 3r + -5r Combine like terms: 3r + -5r = -2r 1 + 2r = 65 + -2r Solving 1 + 2r = 65 + -2r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '2r' to each side of the equation. 1 + 2r + 2r = 65 + -2r + 2r Combine like terms: 2r + 2r = 4r 1 + 4r = 65 + -2r + 2r Combine like terms: -2r + 2r = 0 1 + 4r = 65 + 0 1 + 4r = 65 Add '-1' to each side of the equation. 1 + -1 + 4r = 65 + -1 Combine like terms: 1 + -1 = 0 0 + 4r = 65 + -1 4r = 65 + -1 Combine like terms: 65 + -1 = 64 4r = 64 Divide each side by '4'. r = 16 Simplifying r = 16
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