Pregunta
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Write the inequality using interval notation and illustrate the inequality using the real number line.
.
The inequality represents the interval
(Type your answer in interval notation.)

Ask by Chavez Allan. in the United States
Jan 29,2025

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The inequality is written in interval notation as . On the real number line, this is shown with a closed circle at -3 and an open circle at 5, shading the line between them.

Solución

The inequality can be expressed in interval notation as:

Illustration on the Real Number Line:

Below is a representation of the inequality on the real number line:
<----|=========)---->
    -3         5
  • Closed Circle at -3: Indicates that -3 is included in the interval ( ).
  • Open Circle at 5: Indicates that 5 is not included in the interval ( ).
  • Shaded Line Between -3 and 5: Represents all real numbers x such that .

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Beyond the Answer

The inequality represents the interval . In this interval, -3 is included (hence the square bracket) and 5 is excluded (hence the parenthesis).
On a real number line, you can depict this as a shaded line segment starting from -3 (with a closed dot) extending to just before 5 (with an open dot). The closed dot on -3 indicates that it is part of the solution, while the open dot on 5 shows that it is not included in the interval.

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