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Simplifying -12 = 7(2r + -3) + -1(8r + -5) Reorder the terms: -12 = 7(-3 + 2r) + -1(8r + -5) -12 = (-3 * 7 + 2r * 7) + -1(8r + -5) -12 = (-21 + 14r) + -1(8r + -5) Reorder the terms: -12 = -21 + 14r + -1(-5 + 8r) -12 = -21 + 14r + (-5 * -1 + 8r * -1) -12 = -21 + 14r + (5 + -8r) Reorder the terms: -12 = -21 + 5 + 14r + -8r Combine like terms: -21 + 5 = -16 -12 = -16 + 14r + -8r Combine like terms: 14r + -8r = 6r -12 = -16 + 6r Solving -12 = -16 + 6r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-6r' to each side of the equation. -12 + -6r = -16 + 6r + -6r Combine like terms: 6r + -6r = 0 -12 + -6r = -16 + 0 -12 + -6r = -16 Add '12' to each side of the equation. -12 + 12 + -6r = -16 + 12 Combine like terms: -12 + 12 = 0 0 + -6r = -16 + 12 -6r = -16 + 12 Combine like terms: -16 + 12 = -4 -6r = -4 Divide each side by '-6'. r = 0.6666666667 Simplifying r = 0.6666666667
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