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Write the solution set displayed
on the number line using interval notation.

Write the solution set displayed on the number line using interval notation.-example-1
User Adam Meyer
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1 Answer

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Answer: (-∞, -3) U [1, ∞)

Step-by-step explanation

The portion on the left represents x < -3. The open hole means we don't include -3 itself as part of the solution. This will mean we use a parenthesis.

Think of x < -3 as -∞ < x < -3 to help see how it leads to (-∞, -3)

The portion on the right represents x ≥ 1. This time we have a closed filled in circle endpoint to include x = 1.

Think of x ≥ 1 as 1 ≤ x which expands to 1 ≤ x < ∞, to help see how it leads to [1, ∞)

Use a square bracket to include the endpoint x = 1.

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In summary, the portion on the left is x < -3 which converts to (-∞, -3)

The portion on the right is x ≥ 1 which converts to [1, ∞)

We glue these disjoint intervals together with a union symbol to get the final answer (-∞, -3) U [1, ∞)

The union symbol means "or"

We are either in interval (-∞, -3) OR we are in interval [1, ∞). We cannot be in both intervals at the same time. There isn't any common overlap between the disjoint intervals.

User EarlyPoster
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