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Simplifying 2(3r + -7) + 4(3r + 2) = 6(5r + 9) + 3 Reorder the terms: 2(-7 + 3r) + 4(3r + 2) = 6(5r + 9) + 3 (-7 * 2 + 3r * 2) + 4(3r + 2) = 6(5r + 9) + 3 (-14 + 6r) + 4(3r + 2) = 6(5r + 9) + 3 Reorder the terms: -14 + 6r + 4(2 + 3r) = 6(5r + 9) + 3 -14 + 6r + (2 * 4 + 3r * 4) = 6(5r + 9) + 3 -14 + 6r + (8 + 12r) = 6(5r + 9) + 3 Reorder the terms: -14 + 8 + 6r + 12r = 6(5r + 9) + 3 Combine like terms: -14 + 8 = -6 -6 + 6r + 12r = 6(5r + 9) + 3 Combine like terms: 6r + 12r = 18r -6 + 18r = 6(5r + 9) + 3 Reorder the terms: -6 + 18r = 6(9 + 5r) + 3 -6 + 18r = (9 * 6 + 5r * 6) + 3 -6 + 18r = (54 + 30r) + 3 Reorder the terms: -6 + 18r = 54 + 3 + 30r Combine like terms: 54 + 3 = 57 -6 + 18r = 57 + 30r Solving -6 + 18r = 57 + 30r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-30r' to each side of the equation. -6 + 18r + -30r = 57 + 30r + -30r Combine like terms: 18r + -30r = -12r -6 + -12r = 57 + 30r + -30r Combine like terms: 30r + -30r = 0 -6 + -12r = 57 + 0 -6 + -12r = 57 Add '6' to each side of the equation. -6 + 6 + -12r = 57 + 6 Combine like terms: -6 + 6 = 0 0 + -12r = 57 + 6 -12r = 57 + 6 Combine like terms: 57 + 6 = 63 -12r = 63 Divide each side by '-12'. r = -5.25 Simplifying r = -5.25
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