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Simplifying 6 + -3(2r + -4) + -7r = 12 + -5(r + -2) Reorder the terms: 6 + -3(-4 + 2r) + -7r = 12 + -5(r + -2) 6 + (-4 * -3 + 2r * -3) + -7r = 12 + -5(r + -2) 6 + (12 + -6r) + -7r = 12 + -5(r + -2) Combine like terms: 6 + 12 = 18 18 + -6r + -7r = 12 + -5(r + -2) Combine like terms: -6r + -7r = -13r 18 + -13r = 12 + -5(r + -2) Reorder the terms: 18 + -13r = 12 + -5(-2 + r) 18 + -13r = 12 + (-2 * -5 + r * -5) 18 + -13r = 12 + (10 + -5r) Combine like terms: 12 + 10 = 22 18 + -13r = 22 + -5r Solving 18 + -13r = 22 + -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. 18 + -13r + 5r = 22 + -5r + 5r Combine like terms: -13r + 5r = -8r 18 + -8r = 22 + -5r + 5r Combine like terms: -5r + 5r = 0 18 + -8r = 22 + 0 18 + -8r = 22 Add '-18' to each side of the equation. 18 + -18 + -8r = 22 + -18 Combine like terms: 18 + -18 = 0 0 + -8r = 22 + -18 -8r = 22 + -18 Combine like terms: 22 + -18 = 4 -8r = 4 Divide each side by '-8'. r = -0.5 Simplifying r = -0.5
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