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Simplifying -5(9r + 10) + 5r = 10(r + 10) Reorder the terms: -5(10 + 9r) + 5r = 10(r + 10) (10 * -5 + 9r * -5) + 5r = 10(r + 10) (-50 + -45r) + 5r = 10(r + 10) Combine like terms: -45r + 5r = -40r -50 + -40r = 10(r + 10) Reorder the terms: -50 + -40r = 10(10 + r) -50 + -40r = (10 * 10 + r * 10) -50 + -40r = (100 + 10r) Solving -50 + -40r = 100 + 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. -50 + -40r + -10r = 100 + 10r + -10r Combine like terms: -40r + -10r = -50r -50 + -50r = 100 + 10r + -10r Combine like terms: 10r + -10r = 0 -50 + -50r = 100 + 0 -50 + -50r = 100 Add '50' to each side of the equation. -50 + 50 + -50r = 100 + 50 Combine like terms: -50 + 50 = 0 0 + -50r = 100 + 50 -50r = 100 + 50 Combine like terms: 100 + 50 = 150 -50r = 150 Divide each side by '-50'. r = -3 Simplifying r = -3
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