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Consider two functions \(f\) and \(g\) defined on \(\mathbb{R}\) by:$$ f(x) = \dfrac{3}{4}x - 1 \quad \text{and} \quad g(x) = -\dfrac{1}{4}x + 1 $$The curves \(\mathscr{C}_f\) and \(\mathscr{C}_g\) are shown below, intersecting at point \(C(2, 0.5)\). Two regions are shaded: triangle \(ABC\) (orange) and triangle \(CDE\) (green).
  1. Solve \(f(x) \ge g(x)\) by determining the interval of \(x\) for which the inequality is true.
  2. Express the area of triangle \(ABC\) using an integral and calculate its value.
  3. Express the area of triangle \(CDE\) using an integral and calculate its value.

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