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Simplifying -3.8(1 + 4.2r) = 0.6(1.5 + 8.6r) + -0.5 (1 * -3.8 + 4.2r * -3.8) = 0.6(1.5 + 8.6r) + -0.5 (-3.8 + -15.96r) = 0.6(1.5 + 8.6r) + -0.5 -3.8 + -15.96r = (1.5 * 0.6 + 8.6r * 0.6) + -0.5 -3.8 + -15.96r = (0.9 + 5.16r) + -0.5 Reorder the terms: -3.8 + -15.96r = 0.9 + -0.5 + 5.16r Combine like terms: 0.9 + -0.5 = 0.4 -3.8 + -15.96r = 0.4 + 5.16r Solving -3.8 + -15.96r = 0.4 + 5.16r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-5.16r' to each side of the equation. -3.8 + -15.96r + -5.16r = 0.4 + 5.16r + -5.16r Combine like terms: -15.96r + -5.16r = -21.12r -3.8 + -21.12r = 0.4 + 5.16r + -5.16r Combine like terms: 5.16r + -5.16r = 0.00 -3.8 + -21.12r = 0.4 + 0.00 -3.8 + -21.12r = 0.4 Add '3.8' to each side of the equation. -3.8 + 3.8 + -21.12r = 0.4 + 3.8 Combine like terms: -3.8 + 3.8 = 0.0 0.0 + -21.12r = 0.4 + 3.8 -21.12r = 0.4 + 3.8 Combine like terms: 0.4 + 3.8 = 4.2 -21.12r = 4.2 Divide each side by '-21.12'. r = -0.1988636364 Simplifying r = -0.1988636364
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