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Simplifying -3(4f + 9) + 2(3r + 8) = r + -1(9r + -5) Reorder the terms: -3(9 + 4f) + 2(3r + 8) = r + -1(9r + -5) (9 * -3 + 4f * -3) + 2(3r + 8) = r + -1(9r + -5) (-27 + -12f) + 2(3r + 8) = r + -1(9r + -5) Reorder the terms: -27 + -12f + 2(8 + 3r) = r + -1(9r + -5) -27 + -12f + (8 * 2 + 3r * 2) = r + -1(9r + -5) -27 + -12f + (16 + 6r) = r + -1(9r + -5) Reorder the terms: -27 + 16 + -12f + 6r = r + -1(9r + -5) Combine like terms: -27 + 16 = -11 -11 + -12f + 6r = r + -1(9r + -5) Reorder the terms: -11 + -12f + 6r = r + -1(-5 + 9r) -11 + -12f + 6r = r + (-5 * -1 + 9r * -1) -11 + -12f + 6r = r + (5 + -9r) Reorder the terms: -11 + -12f + 6r = 5 + r + -9r Combine like terms: r + -9r = -8r -11 + -12f + 6r = 5 + -8r Solving -11 + -12f + 6r = 5 + -8r Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '11' to each side of the equation. -11 + -12f + 11 + 6r = 5 + 11 + -8r Reorder the terms: -11 + 11 + -12f + 6r = 5 + 11 + -8r Combine like terms: -11 + 11 = 0 0 + -12f + 6r = 5 + 11 + -8r -12f + 6r = 5 + 11 + -8r Combine like terms: 5 + 11 = 16 -12f + 6r = 16 + -8r Add '-6r' to each side of the equation. -12f + 6r + -6r = 16 + -8r + -6r Combine like terms: 6r + -6r = 0 -12f + 0 = 16 + -8r + -6r -12f = 16 + -8r + -6r Combine like terms: -8r + -6r = -14r -12f = 16 + -14r Divide each side by '-12'. f = -1.333333333 + 1.166666667r Simplifying f = -1.333333333 + 1.166666667r
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