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Simplifying 8(r + 2) + 6(r + -3) = 6(2r + 8) Reorder the terms: 8(2 + r) + 6(r + -3) = 6(2r + 8) (2 * 8 + r * 8) + 6(r + -3) = 6(2r + 8) (16 + 8r) + 6(r + -3) = 6(2r + 8) Reorder the terms: 16 + 8r + 6(-3 + r) = 6(2r + 8) 16 + 8r + (-3 * 6 + r * 6) = 6(2r + 8) 16 + 8r + (-18 + 6r) = 6(2r + 8) Reorder the terms: 16 + -18 + 8r + 6r = 6(2r + 8) Combine like terms: 16 + -18 = -2 -2 + 8r + 6r = 6(2r + 8) Combine like terms: 8r + 6r = 14r -2 + 14r = 6(2r + 8) Reorder the terms: -2 + 14r = 6(8 + 2r) -2 + 14r = (8 * 6 + 2r * 6) -2 + 14r = (48 + 12r) Solving -2 + 14r = 48 + 12r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-12r' to each side of the equation. -2 + 14r + -12r = 48 + 12r + -12r Combine like terms: 14r + -12r = 2r -2 + 2r = 48 + 12r + -12r Combine like terms: 12r + -12r = 0 -2 + 2r = 48 + 0 -2 + 2r = 48 Add '2' to each side of the equation. -2 + 2 + 2r = 48 + 2 Combine like terms: -2 + 2 = 0 0 + 2r = 48 + 2 2r = 48 + 2 Combine like terms: 48 + 2 = 50 2r = 50 Divide each side by '2'. r = 25 Simplifying r = 25
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