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Simplifying 3 + 5r + 4(1 + -1r) = 1 + 3r 3 + 5r + (1 * 4 + -1r * 4) = 1 + 3r 3 + 5r + (4 + -4r) = 1 + 3r Reorder the terms: 3 + 4 + 5r + -4r = 1 + 3r Combine like terms: 3 + 4 = 7 7 + 5r + -4r = 1 + 3r Combine like terms: 5r + -4r = 1r 7 + 1r = 1 + 3r Solving 7 + 1r = 1 + 3r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-3r' to each side of the equation. 7 + 1r + -3r = 1 + 3r + -3r Combine like terms: 1r + -3r = -2r 7 + -2r = 1 + 3r + -3r Combine like terms: 3r + -3r = 0 7 + -2r = 1 + 0 7 + -2r = 1 Add '-7' to each side of the equation. 7 + -7 + -2r = 1 + -7 Combine like terms: 7 + -7 = 0 0 + -2r = 1 + -7 -2r = 1 + -7 Combine like terms: 1 + -7 = -6 -2r = -6 Divide each side by '-2'. r = 3 Simplifying r = 3
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