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Simplifying -7 = -1(1 + -2r) + 2(1 + -3r) -7 = (1 * -1 + -2r * -1) + 2(1 + -3r) -7 = (-1 + 2r) + 2(1 + -3r) -7 = -1 + 2r + (1 * 2 + -3r * 2) -7 = -1 + 2r + (2 + -6r) Reorder the terms: -7 = -1 + 2 + 2r + -6r Combine like terms: -1 + 2 = 1 -7 = 1 + 2r + -6r Combine like terms: 2r + -6r = -4r -7 = 1 + -4r Solving -7 = 1 + -4r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '4r' to each side of the equation. -7 + 4r = 1 + -4r + 4r Combine like terms: -4r + 4r = 0 -7 + 4r = 1 + 0 -7 + 4r = 1 Add '7' to each side of the equation. -7 + 7 + 4r = 1 + 7 Combine like terms: -7 + 7 = 0 0 + 4r = 1 + 7 4r = 1 + 7 Combine like terms: 1 + 7 = 8 4r = 8 Divide each side by '4'. r = 2 Simplifying r = 2
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