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Simplifying -31 = 5(1 + -4r) + 4(r + -1) -31 = (1 * 5 + -4r * 5) + 4(r + -1) -31 = (5 + -20r) + 4(r + -1) Reorder the terms: -31 = 5 + -20r + 4(-1 + r) -31 = 5 + -20r + (-1 * 4 + r * 4) -31 = 5 + -20r + (-4 + 4r) Reorder the terms: -31 = 5 + -4 + -20r + 4r Combine like terms: 5 + -4 = 1 -31 = 1 + -20r + 4r Combine like terms: -20r + 4r = -16r -31 = 1 + -16r Solving -31 = 1 + -16r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '16r' to each side of the equation. -31 + 16r = 1 + -16r + 16r Combine like terms: -16r + 16r = 0 -31 + 16r = 1 + 0 -31 + 16r = 1 Add '31' to each side of the equation. -31 + 31 + 16r = 1 + 31 Combine like terms: -31 + 31 = 0 0 + 16r = 1 + 31 16r = 1 + 31 Combine like terms: 1 + 31 = 32 16r = 32 Divide each side by '16'. r = 2 Simplifying r = 2
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