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Simplifying 0.4(100 + 20r) = 42 + -12r (100 * 0.4 + 20r * 0.4) = 42 + -12r (40 + 8r) = 42 + -12r Solving 40 + 8r = 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. 40 + 8r + 12r = 42 + -12r + 12r Combine like terms: 8r + 12r = 20r 40 + 20r = 42 + -12r + 12r Combine like terms: -12r + 12r = 0 40 + 20r = 42 + 0 40 + 20r = 42 Add '-40' to each side of the equation. 40 + -40 + 20r = 42 + -40 Combine like terms: 40 + -40 = 0 0 + 20r = 42 + -40 20r = 42 + -40 Combine like terms: 42 + -40 = 2 20r = 2 Divide each side by '20'. r = 0.1 Simplifying r = 0.1
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