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Simplifying -5(10r + 2) + 3(6r + 8) = 0 Reorder the terms: -5(2 + 10r) + 3(6r + 8) = 0 (2 * -5 + 10r * -5) + 3(6r + 8) = 0 (-10 + -50r) + 3(6r + 8) = 0 Reorder the terms: -10 + -50r + 3(8 + 6r) = 0 -10 + -50r + (8 * 3 + 6r * 3) = 0 -10 + -50r + (24 + 18r) = 0 Reorder the terms: -10 + 24 + -50r + 18r = 0 Combine like terms: -10 + 24 = 14 14 + -50r + 18r = 0 Combine like terms: -50r + 18r = -32r 14 + -32r = 0 Solving 14 + -32r = 0 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + -32r = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -32r = 0 + -14 -32r = 0 + -14 Combine like terms: 0 + -14 = -14 -32r = -14 Divide each side by '-32'. r = 0.4375 Simplifying r = 0.4375
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