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Simplifying -3(4r + 3) + 4(6r + 1) = 43 Reorder the terms: -3(3 + 4r) + 4(6r + 1) = 43 (3 * -3 + 4r * -3) + 4(6r + 1) = 43 (-9 + -12r) + 4(6r + 1) = 43 Reorder the terms: -9 + -12r + 4(1 + 6r) = 43 -9 + -12r + (1 * 4 + 6r * 4) = 43 -9 + -12r + (4 + 24r) = 43 Reorder the terms: -9 + 4 + -12r + 24r = 43 Combine like terms: -9 + 4 = -5 -5 + -12r + 24r = 43 Combine like terms: -12r + 24r = 12r -5 + 12r = 43 Solving -5 + 12r = 43 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + 12r = 43 + 5 Combine like terms: -5 + 5 = 0 0 + 12r = 43 + 5 12r = 43 + 5 Combine like terms: 43 + 5 = 48 12r = 48 Divide each side by '12'. r = 4 Simplifying r = 4
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