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Simplifying 3(r + -5) + 2(r + -4) = -2(r + -1) + 8(r + 2) Reorder the terms: 3(-5 + r) + 2(r + -4) = -2(r + -1) + 8(r + 2) (-5 * 3 + r * 3) + 2(r + -4) = -2(r + -1) + 8(r + 2) (-15 + 3r) + 2(r + -4) = -2(r + -1) + 8(r + 2) Reorder the terms: -15 + 3r + 2(-4 + r) = -2(r + -1) + 8(r + 2) -15 + 3r + (-4 * 2 + r * 2) = -2(r + -1) + 8(r + 2) -15 + 3r + (-8 + 2r) = -2(r + -1) + 8(r + 2) Reorder the terms: -15 + -8 + 3r + 2r = -2(r + -1) + 8(r + 2) Combine like terms: -15 + -8 = -23 -23 + 3r + 2r = -2(r + -1) + 8(r + 2) Combine like terms: 3r + 2r = 5r -23 + 5r = -2(r + -1) + 8(r + 2) Reorder the terms: -23 + 5r = -2(-1 + r) + 8(r + 2) -23 + 5r = (-1 * -2 + r * -2) + 8(r + 2) -23 + 5r = (2 + -2r) + 8(r + 2) Reorder the terms: -23 + 5r = 2 + -2r + 8(2 + r) -23 + 5r = 2 + -2r + (2 * 8 + r * 8) -23 + 5r = 2 + -2r + (16 + 8r) Reorder the terms: -23 + 5r = 2 + 16 + -2r + 8r Combine like terms: 2 + 16 = 18 -23 + 5r = 18 + -2r + 8r Combine like terms: -2r + 8r = 6r -23 + 5r = 18 + 6r Solving -23 + 5r = 18 + 6r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-6r' to each side of the equation. -23 + 5r + -6r = 18 + 6r + -6r Combine like terms: 5r + -6r = -1r -23 + -1r = 18 + 6r + -6r Combine like terms: 6r + -6r = 0 -23 + -1r = 18 + 0 -23 + -1r = 18 Add '23' to each side of the equation. -23 + 23 + -1r = 18 + 23 Combine like terms: -23 + 23 = 0 0 + -1r = 18 + 23 -1r = 18 + 23 Combine like terms: 18 + 23 = 41 -1r = 41 Divide each side by '-1'. r = -41 Simplifying r = -41
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