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Simplifying 54 = 6(3 + -4r) + -4(1 + -1r) 54 = (3 * 6 + -4r * 6) + -4(1 + -1r) 54 = (18 + -24r) + -4(1 + -1r) 54 = 18 + -24r + (1 * -4 + -1r * -4) 54 = 18 + -24r + (-4 + 4r) Reorder the terms: 54 = 18 + -4 + -24r + 4r Combine like terms: 18 + -4 = 14 54 = 14 + -24r + 4r Combine like terms: -24r + 4r = -20r 54 = 14 + -20r Solving 54 = 14 + -20r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '20r' to each side of the equation. 54 + 20r = 14 + -20r + 20r Combine like terms: -20r + 20r = 0 54 + 20r = 14 + 0 54 + 20r = 14 Add '-54' to each side of the equation. 54 + -54 + 20r = 14 + -54 Combine like terms: 54 + -54 = 0 0 + 20r = 14 + -54 20r = 14 + -54 Combine like terms: 14 + -54 = -40 20r = -40 Divide each side by '20'. r = -2 Simplifying r = -2
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