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Simplifying -7(r + 6) + 12(3 + -4r) = 1 + 2r + 5r + -7 Reorder the terms: -7(6 + r) + 12(3 + -4r) = 1 + 2r + 5r + -7 (6 * -7 + r * -7) + 12(3 + -4r) = 1 + 2r + 5r + -7 (-42 + -7r) + 12(3 + -4r) = 1 + 2r + 5r + -7 -42 + -7r + (3 * 12 + -4r * 12) = 1 + 2r + 5r + -7 -42 + -7r + (36 + -48r) = 1 + 2r + 5r + -7 Reorder the terms: -42 + 36 + -7r + -48r = 1 + 2r + 5r + -7 Combine like terms: -42 + 36 = -6 -6 + -7r + -48r = 1 + 2r + 5r + -7 Combine like terms: -7r + -48r = -55r -6 + -55r = 1 + 2r + 5r + -7 Reorder the terms: -6 + -55r = 1 + -7 + 2r + 5r Combine like terms: 1 + -7 = -6 -6 + -55r = -6 + 2r + 5r Combine like terms: 2r + 5r = 7r -6 + -55r = -6 + 7r Add '6' to each side of the equation. -6 + 6 + -55r = -6 + 6 + 7r Combine like terms: -6 + 6 = 0 0 + -55r = -6 + 6 + 7r -55r = -6 + 6 + 7r Combine like terms: -6 + 6 = 0 -55r = 0 + 7r -55r = 7r Solving -55r = 7r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-7r' to each side of the equation. -55r + -7r = 7r + -7r Combine like terms: -55r + -7r = -62r -62r = 7r + -7r Combine like terms: 7r + -7r = 0 -62r = 0 Divide each side by '-62'. r = 0 Simplifying r = 0
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