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Simplifying 7r + 6(r + -2) = 4r + 10(2r + 1) Reorder the terms: 7r + 6(-2 + r) = 4r + 10(2r + 1) 7r + (-2 * 6 + r * 6) = 4r + 10(2r + 1) 7r + (-12 + 6r) = 4r + 10(2r + 1) Reorder the terms: -12 + 7r + 6r = 4r + 10(2r + 1) Combine like terms: 7r + 6r = 13r -12 + 13r = 4r + 10(2r + 1) Reorder the terms: -12 + 13r = 4r + 10(1 + 2r) -12 + 13r = 4r + (1 * 10 + 2r * 10) -12 + 13r = 4r + (10 + 20r) Reorder the terms: -12 + 13r = 10 + 4r + 20r Combine like terms: 4r + 20r = 24r -12 + 13r = 10 + 24r Solving -12 + 13r = 10 + 24r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-24r' to each side of the equation. -12 + 13r + -24r = 10 + 24r + -24r Combine like terms: 13r + -24r = -11r -12 + -11r = 10 + 24r + -24r Combine like terms: 24r + -24r = 0 -12 + -11r = 10 + 0 -12 + -11r = 10 Add '12' to each side of the equation. -12 + 12 + -11r = 10 + 12 Combine like terms: -12 + 12 = 0 0 + -11r = 10 + 12 -11r = 10 + 12 Combine like terms: 10 + 12 = 22 -11r = 22 Divide each side by '-11'. r = -2 Simplifying r = -2
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