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