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Simplifying 8r + -1(12 + -3r) = 19 + 3(4r + -6) 8r + (12 * -1 + -3r * -1) = 19 + 3(4r + -6) 8r + (-12 + 3r) = 19 + 3(4r + -6) Reorder the terms: -12 + 8r + 3r = 19 + 3(4r + -6) Combine like terms: 8r + 3r = 11r -12 + 11r = 19 + 3(4r + -6) Reorder the terms: -12 + 11r = 19 + 3(-6 + 4r) -12 + 11r = 19 + (-6 * 3 + 4r * 3) -12 + 11r = 19 + (-18 + 12r) Combine like terms: 19 + -18 = 1 -12 + 11r = 1 + 12r Solving -12 + 11r = 1 + 12r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-12r' to each side of the equation. -12 + 11r + -12r = 1 + 12r + -12r Combine like terms: 11r + -12r = -1r -12 + -1r = 1 + 12r + -12r Combine like terms: 12r + -12r = 0 -12 + -1r = 1 + 0 -12 + -1r = 1 Add '12' to each side of the equation. -12 + 12 + -1r = 1 + 12 Combine like terms: -12 + 12 = 0 0 + -1r = 1 + 12 -1r = 1 + 12 Combine like terms: 1 + 12 = 13 -1r = 13 Divide each side by '-1'. r = -13 Simplifying r = -13
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