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Write the inequality represented by the unshaded region in the given graphs.

Mathematics

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Answers

2 parts
a

x≥−2x \ge -2

b

y≥−2y \ge -2

Step-by-step solution

4 steps

To write the inequality represented by the unshaded region, we first identify the boundary line and then determine the correct inequality sign based on the unshaded area.

Part a· 2 steps

  1. Identify the boundary line.

    The graph shows a solid vertical line passing through x=−2x = -2. This means the inequality will involve xx and include "or equal to".

  2. Determine the unshaded region.

    The shaded region is to the left of the line (x<−2x < -2). The unshaded region is to the right of the line, including the line itself.
    Therefore, the inequality for the unshaded region is x≥−2x \ge -2.
    The inequality is x≥−2\boxed{x \ge -2}.

Part b

y≥−2y \ge -2

  1. Identify the boundary line.

    The graph shows a solid horizontal line passing through y=−2y = -2. This means the inequality will involve yy and include "or equal to".

  2. Determine the unshaded region.

    The shaded region is below the line (y<−2y < -2). The unshaded region is above the line, including the line itself.
    Therefore, the inequality for the unshaded region is y≥−2y \ge -2.
    The inequality is y≥−2\boxed{y \ge -2}.

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