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Simplifying -1(1 + -2r) + -8(5r + 3) = 51 (1 * -1 + -2r * -1) + -8(5r + 3) = 51 (-1 + 2r) + -8(5r + 3) = 51 Reorder the terms: -1 + 2r + -8(3 + 5r) = 51 -1 + 2r + (3 * -8 + 5r * -8) = 51 -1 + 2r + (-24 + -40r) = 51 Reorder the terms: -1 + -24 + 2r + -40r = 51 Combine like terms: -1 + -24 = -25 -25 + 2r + -40r = 51 Combine like terms: 2r + -40r = -38r -25 + -38r = 51 Solving -25 + -38r = 51 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + -38r = 51 + 25 Combine like terms: -25 + 25 = 0 0 + -38r = 51 + 25 -38r = 51 + 25 Combine like terms: 51 + 25 = 76 -38r = 76 Divide each side by '-38'. r = -2 Simplifying r = -2
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