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Simplifying 7[9 + -3(-2r + -4)] = 12r + 42 Reorder the terms: 7[9 + -3(-4 + -2r)] = 12r + 42 7[9 + (-4 * -3 + -2r * -3)] = 12r + 42 7[9 + (12 + 6r)] = 12r + 42 Combine like terms: 9 + 12 = 21 7[21 + 6r] = 12r + 42 [21 * 7 + 6r * 7] = 12r + 42 [147 + 42r] = 12r + 42 Reorder the terms: 147 + 42r = 42 + 12r Solving 147 + 42r = 42 + 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. 147 + 42r + -12r = 42 + 12r + -12r Combine like terms: 42r + -12r = 30r 147 + 30r = 42 + 12r + -12r Combine like terms: 12r + -12r = 0 147 + 30r = 42 + 0 147 + 30r = 42 Add '-147' to each side of the equation. 147 + -147 + 30r = 42 + -147 Combine like terms: 147 + -147 = 0 0 + 30r = 42 + -147 30r = 42 + -147 Combine like terms: 42 + -147 = -105 30r = -105 Divide each side by '30'. r = -3.5 Simplifying r = -3.5
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