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Exercises · Q9

Q.Draw the graphical solution of x≥2x\ge 2 in the coordinate plane.

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✓ Free question

In the coordinate plane, the equation x=2x=2 (with yy free) is the vertical line through (2,0)(2,0) parallel to the yy-axis.

Solid or dashed: the sign is ≥\ge (weak), so the line x=2x=2 is solid and included.

Which side: every point with first coordinate greater than 22 satisfies x≥2x\ge2, so the solution is the region to the right of the line. Testing the origin confirms it: x=0x=0 gives 0≥20\ge2, false, so the origin's side (the left) is not the solution — shade the opposite side, the right.

Figure 5 — Graphical solution of x ≥ 2 in the plane: the closed half-plane to the right of the solid vertical line x=2
Figure 5 — Graphical solution of x ≥ 2 in the plane: the closed half-plane to the right of the solid vertical line x=2

Check (independent verification): (3,5)(3,5) has x=3≥2x=3\ge2 ✓ inside; (2,−1)(2,-1) has x=2≥2x=2\ge2 ✓ on the included line; (1,0)(1,0) has x=1≥2x=1\ge2 false ✓ outside.

✓Final answer

The closed half-plane {(x,y):x≥2}\{(x,y):x\ge2\} — everything on and to the right of the solid vertical line x=2x=2.

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