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Simplifying 12.4(2f + -5) + -11.6(3f + -2) + 3.4(0.5f + 2) = 0 Reorder the terms: 12.4(-5 + 2f) + -11.6(3f + -2) + 3.4(0.5f + 2) = 0 (-5 * 12.4 + 2f * 12.4) + -11.6(3f + -2) + 3.4(0.5f + 2) = 0 (-62 + 24.8f) + -11.6(3f + -2) + 3.4(0.5f + 2) = 0 Reorder the terms: -62 + 24.8f + -11.6(-2 + 3f) + 3.4(0.5f + 2) = 0 -62 + 24.8f + (-2 * -11.6 + 3f * -11.6) + 3.4(0.5f + 2) = 0 -62 + 24.8f + (23.2 + -34.8f) + 3.4(0.5f + 2) = 0 Reorder the terms: -62 + 24.8f + 23.2 + -34.8f + 3.4(2 + 0.5f) = 0 -62 + 24.8f + 23.2 + -34.8f + (2 * 3.4 + 0.5f * 3.4) = 0 -62 + 24.8f + 23.2 + -34.8f + (6.8 + 1.7f) = 0 Reorder the terms: -62 + 23.2 + 6.8 + 24.8f + -34.8f + 1.7f = 0 Combine like terms: -62 + 23.2 = -38.8 -38.8 + 6.8 + 24.8f + -34.8f + 1.7f = 0 Combine like terms: -38.8 + 6.8 = -32 -32 + 24.8f + -34.8f + 1.7f = 0 Combine like terms: 24.8f + -34.8f = -10f -32 + -10f + 1.7f = 0 Combine like terms: -10f + 1.7f = -8.3f -32 + -8.3f = 0 Solving -32 + -8.3f = 0 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '32' to each side of the equation. -32 + 32 + -8.3f = 0 + 32 Combine like terms: -32 + 32 = 0 0 + -8.3f = 0 + 32 -8.3f = 0 + 32 Combine like terms: 0 + 32 = 32 -8.3f = 32 Divide each side by '-8.3'. f = -3.855421687 Simplifying f = -3.855421687
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