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Simplifying 1 + -5r + -3r = 7(8r + -1) + -1(-3r + 6) Combine like terms: -5r + -3r = -8r 1 + -8r = 7(8r + -1) + -1(-3r + 6) Reorder the terms: 1 + -8r = 7(-1 + 8r) + -1(-3r + 6) 1 + -8r = (-1 * 7 + 8r * 7) + -1(-3r + 6) 1 + -8r = (-7 + 56r) + -1(-3r + 6) Reorder the terms: 1 + -8r = -7 + 56r + -1(6 + -3r) 1 + -8r = -7 + 56r + (6 * -1 + -3r * -1) 1 + -8r = -7 + 56r + (-6 + 3r) Reorder the terms: 1 + -8r = -7 + -6 + 56r + 3r Combine like terms: -7 + -6 = -13 1 + -8r = -13 + 56r + 3r Combine like terms: 56r + 3r = 59r 1 + -8r = -13 + 59r Solving 1 + -8r = -13 + 59r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-59r' to each side of the equation. 1 + -8r + -59r = -13 + 59r + -59r Combine like terms: -8r + -59r = -67r 1 + -67r = -13 + 59r + -59r Combine like terms: 59r + -59r = 0 1 + -67r = -13 + 0 1 + -67r = -13 Add '-1' to each side of the equation. 1 + -1 + -67r = -13 + -1 Combine like terms: 1 + -1 = 0 0 + -67r = -13 + -1 -67r = -13 + -1 Combine like terms: -13 + -1 = -14 -67r = -14 Divide each side by '-67'. r = 0.2089552239 Simplifying r = 0.2089552239
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