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Simplifying -19 = -5(7r + 2) + 8(6r + -6) Reorder the terms: -19 = -5(2 + 7r) + 8(6r + -6) -19 = (2 * -5 + 7r * -5) + 8(6r + -6) -19 = (-10 + -35r) + 8(6r + -6) Reorder the terms: -19 = -10 + -35r + 8(-6 + 6r) -19 = -10 + -35r + (-6 * 8 + 6r * 8) -19 = -10 + -35r + (-48 + 48r) Reorder the terms: -19 = -10 + -48 + -35r + 48r Combine like terms: -10 + -48 = -58 -19 = -58 + -35r + 48r Combine like terms: -35r + 48r = 13r -19 = -58 + 13r Solving -19 = -58 + 13r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-13r' to each side of the equation. -19 + -13r = -58 + 13r + -13r Combine like terms: 13r + -13r = 0 -19 + -13r = -58 + 0 -19 + -13r = -58 Add '19' to each side of the equation. -19 + 19 + -13r = -58 + 19 Combine like terms: -19 + 19 = 0 0 + -13r = -58 + 19 -13r = -58 + 19 Combine like terms: -58 + 19 = -39 -13r = -39 Divide each side by '-13'. r = 3 Simplifying r = 3
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