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Simplifying r + -8 + -9r = 4(1 + 10r) + -5(1 + 11r) Reorder the terms: -8 + r + -9r = 4(1 + 10r) + -5(1 + 11r) Combine like terms: r + -9r = -8r -8 + -8r = 4(1 + 10r) + -5(1 + 11r) -8 + -8r = (1 * 4 + 10r * 4) + -5(1 + 11r) -8 + -8r = (4 + 40r) + -5(1 + 11r) -8 + -8r = 4 + 40r + (1 * -5 + 11r * -5) -8 + -8r = 4 + 40r + (-5 + -55r) Reorder the terms: -8 + -8r = 4 + -5 + 40r + -55r Combine like terms: 4 + -5 = -1 -8 + -8r = -1 + 40r + -55r Combine like terms: 40r + -55r = -15r -8 + -8r = -1 + -15r Solving -8 + -8r = -1 + -15r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '15r' to each side of the equation. -8 + -8r + 15r = -1 + -15r + 15r Combine like terms: -8r + 15r = 7r -8 + 7r = -1 + -15r + 15r Combine like terms: -15r + 15r = 0 -8 + 7r = -1 + 0 -8 + 7r = -1 Add '8' to each side of the equation. -8 + 8 + 7r = -1 + 8 Combine like terms: -8 + 8 = 0 0 + 7r = -1 + 8 7r = -1 + 8 Combine like terms: -1 + 8 = 7 7r = 7 Divide each side by '7'. r = 1 Simplifying r = 1
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