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Simplifying 5r + 5 + -4 = -1(r + 3) + 4(2r + -2) Reorder the terms: 5 + -4 + 5r = -1(r + 3) + 4(2r + -2) Combine like terms: 5 + -4 = 1 1 + 5r = -1(r + 3) + 4(2r + -2) Reorder the terms: 1 + 5r = -1(3 + r) + 4(2r + -2) 1 + 5r = (3 * -1 + r * -1) + 4(2r + -2) 1 + 5r = (-3 + -1r) + 4(2r + -2) Reorder the terms: 1 + 5r = -3 + -1r + 4(-2 + 2r) 1 + 5r = -3 + -1r + (-2 * 4 + 2r * 4) 1 + 5r = -3 + -1r + (-8 + 8r) Reorder the terms: 1 + 5r = -3 + -8 + -1r + 8r Combine like terms: -3 + -8 = -11 1 + 5r = -11 + -1r + 8r Combine like terms: -1r + 8r = 7r 1 + 5r = -11 + 7r Solving 1 + 5r = -11 + 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. 1 + 5r + -7r = -11 + 7r + -7r Combine like terms: 5r + -7r = -2r 1 + -2r = -11 + 7r + -7r Combine like terms: 7r + -7r = 0 1 + -2r = -11 + 0 1 + -2r = -11 Add '-1' to each side of the equation. 1 + -1 + -2r = -11 + -1 Combine like terms: 1 + -1 = 0 0 + -2r = -11 + -1 -2r = -11 + -1 Combine like terms: -11 + -1 = -12 -2r = -12 Divide each side by '-2'. r = 6 Simplifying r = 6
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