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Simplifying 0.2(5 + -2r) = 0.3(1 + -1r) (5 * 0.2 + -2r * 0.2) = 0.3(1 + -1r) (1 + -0.4r) = 0.3(1 + -1r) 1 + -0.4r = (1 * 0.3 + -1r * 0.3) 1 + -0.4r = (0.3 + -0.3r) Solving 1 + -0.4r = 0.3 + -0.3r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.3r' to each side of the equation. 1 + -0.4r + 0.3r = 0.3 + -0.3r + 0.3r Combine like terms: -0.4r + 0.3r = -0.1r 1 + -0.1r = 0.3 + -0.3r + 0.3r Combine like terms: -0.3r + 0.3r = 0.0 1 + -0.1r = 0.3 + 0.0 1 + -0.1r = 0.3 Add '-1' to each side of the equation. 1 + -1 + -0.1r = 0.3 + -1 Combine like terms: 1 + -1 = 0 0 + -0.1r = 0.3 + -1 -0.1r = 0.3 + -1 Combine like terms: 0.3 + -1 = -0.7 -0.1r = -0.7 Divide each side by '-0.1'. r = 7 Simplifying r = 7
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