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Simplifying 8(1 + -1r) = 7(6r + -6) (1 * 8 + -1r * 8) = 7(6r + -6) (8 + -8r) = 7(6r + -6) Reorder the terms: 8 + -8r = 7(-6 + 6r) 8 + -8r = (-6 * 7 + 6r * 7) 8 + -8r = (-42 + 42r) Solving 8 + -8r = -42 + 42r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-42r' to each side of the equation. 8 + -8r + -42r = -42 + 42r + -42r Combine like terms: -8r + -42r = -50r 8 + -50r = -42 + 42r + -42r Combine like terms: 42r + -42r = 0 8 + -50r = -42 + 0 8 + -50r = -42 Add '-8' to each side of the equation. 8 + -8 + -50r = -42 + -8 Combine like terms: 8 + -8 = 0 0 + -50r = -42 + -8 -50r = -42 + -8 Combine like terms: -42 + -8 = -50 -50r = -50 Divide each side by '-50'. r = 1 Simplifying r = 1
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