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Simplifying 4(3 + -1r) = 5(2r + 1) (3 * 4 + -1r * 4) = 5(2r + 1) (12 + -4r) = 5(2r + 1) Reorder the terms: 12 + -4r = 5(1 + 2r) 12 + -4r = (1 * 5 + 2r * 5) 12 + -4r = (5 + 10r) Solving 12 + -4r = 5 + 10r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-10r' to each side of the equation. 12 + -4r + -10r = 5 + 10r + -10r Combine like terms: -4r + -10r = -14r 12 + -14r = 5 + 10r + -10r Combine like terms: 10r + -10r = 0 12 + -14r = 5 + 0 12 + -14r = 5 Add '-12' to each side of the equation. 12 + -12 + -14r = 5 + -12 Combine like terms: 12 + -12 = 0 0 + -14r = 5 + -12 -14r = 5 + -12 Combine like terms: 5 + -12 = -7 -14r = -7 Divide each side by '-14'. r = 0.5 Simplifying r = 0.5
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