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Simplifying 2(3r + -7) + 4(3r + 2) = (5r + 9) + 3 Reorder the terms: 2(-7 + 3r) + 4(3r + 2) = (5r + 9) + 3 (-7 * 2 + 3r * 2) + 4(3r + 2) = (5r + 9) + 3 (-14 + 6r) + 4(3r + 2) = (5r + 9) + 3 Reorder the terms: -14 + 6r + 4(2 + 3r) = (5r + 9) + 3 -14 + 6r + (2 * 4 + 3r * 4) = (5r + 9) + 3 -14 + 6r + (8 + 12r) = (5r + 9) + 3 Reorder the terms: -14 + 8 + 6r + 12r = (5r + 9) + 3 Combine like terms: -14 + 8 = -6 -6 + 6r + 12r = (5r + 9) + 3 Combine like terms: 6r + 12r = 18r -6 + 18r = (5r + 9) + 3 Reorder the terms: -6 + 18r = (9 + 5r) + 3 Remove parenthesis around (9 + 5r) -6 + 18r = 9 + 5r + 3 Reorder the terms: -6 + 18r = 9 + 3 + 5r Combine like terms: 9 + 3 = 12 -6 + 18r = 12 + 5r Solving -6 + 18r = 12 + 5r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-5r' to each side of the equation. -6 + 18r + -5r = 12 + 5r + -5r Combine like terms: 18r + -5r = 13r -6 + 13r = 12 + 5r + -5r Combine like terms: 5r + -5r = 0 -6 + 13r = 12 + 0 -6 + 13r = 12 Add '6' to each side of the equation. -6 + 6 + 13r = 12 + 6 Combine like terms: -6 + 6 = 0 0 + 13r = 12 + 6 13r = 12 + 6 Combine like terms: 12 + 6 = 18 13r = 18 Divide each side by '13'. r = 1.384615385 Simplifying r = 1.384615385
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