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Simplifying 11f + 3h + 8 = 12f + h + 15 Reorder the terms: 8 + 11f + 3h = 12f + h + 15 Reorder the terms: 8 + 11f + 3h = 15 + 12f + h Solving 8 + 11f + 3h = 15 + 12f + h Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '-12f' to each side of the equation. 8 + 11f + -12f + 3h = 15 + 12f + -12f + h Combine like terms: 11f + -12f = -1f 8 + -1f + 3h = 15 + 12f + -12f + h Combine like terms: 12f + -12f = 0 8 + -1f + 3h = 15 + 0 + h 8 + -1f + 3h = 15 + h Add '-8' to each side of the equation. 8 + -1f + -8 + 3h = 15 + -8 + h Reorder the terms: 8 + -8 + -1f + 3h = 15 + -8 + h Combine like terms: 8 + -8 = 0 0 + -1f + 3h = 15 + -8 + h -1f + 3h = 15 + -8 + h Combine like terms: 15 + -8 = 7 -1f + 3h = 7 + h Add '-3h' to each side of the equation. -1f + 3h + -3h = 7 + h + -3h Combine like terms: 3h + -3h = 0 -1f + 0 = 7 + h + -3h -1f = 7 + h + -3h Combine like terms: h + -3h = -2h -1f = 7 + -2h Divide each side by '-1'. f = -7 + 2h Simplifying f = -7 + 2h
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