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Simplifying -40 = 5(r + 7) + 5(1 + r) Reorder the terms: -40 = 5(7 + r) + 5(1 + r) -40 = (7 * 5 + r * 5) + 5(1 + r) -40 = (35 + 5r) + 5(1 + r) -40 = 35 + 5r + (1 * 5 + r * 5) -40 = 35 + 5r + (5 + 5r) Reorder the terms: -40 = 35 + 5 + 5r + 5r Combine like terms: 35 + 5 = 40 -40 = 40 + 5r + 5r Combine like terms: 5r + 5r = 10r -40 = 40 + 10r Solving -40 = 40 + 10r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-10r' to each side of the equation. -40 + -10r = 40 + 10r + -10r Combine like terms: 10r + -10r = 0 -40 + -10r = 40 + 0 -40 + -10r = 40 Add '40' to each side of the equation. -40 + 40 + -10r = 40 + 40 Combine like terms: -40 + 40 = 0 0 + -10r = 40 + 40 -10r = 40 + 40 Combine like terms: 40 + 40 = 80 -10r = 80 Divide each side by '-10'. r = -8 Simplifying r = -8
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