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Simplifying 1.5(4 + f) + 2.5(5 + -1f) = 15.7 (4 * 1.5 + f * 1.5) + 2.5(5 + -1f) = 15.7 (6 + 1.5f) + 2.5(5 + -1f) = 15.7 6 + 1.5f + (5 * 2.5 + -1f * 2.5) = 15.7 6 + 1.5f + (12.5 + -2.5f) = 15.7 Reorder the terms: 6 + 12.5 + 1.5f + -2.5f = 15.7 Combine like terms: 6 + 12.5 = 18.5 18.5 + 1.5f + -2.5f = 15.7 Combine like terms: 1.5f + -2.5f = -1f 18.5 + -1f = 15.7 Solving 18.5 + -1f = 15.7 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '-18.5' to each side of the equation. 18.5 + -18.5 + -1f = 15.7 + -18.5 Combine like terms: 18.5 + -18.5 = 0.0 0.0 + -1f = 15.7 + -18.5 -1f = 15.7 + -18.5 Combine like terms: 15.7 + -18.5 = -2.8 -1f = -2.8 Divide each side by '-1'. f = 2.8 Simplifying f = 2.8
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