Express the given set in interval notation and graph. { \left\lbrace\right. x x ∣ | x ≤ 7 x\le7 } \}

Hey y'all, let's take a look at this practice problem. So I want to express the given set in interval notation and then graph it on a number line. And here my set is x is less than or equal to 7. Now in interval notation, since x is less than or equal to 7, I know that one of my endpoints is going to be 7 and since it can go all the way anything less than 7, my other endpoint is a negative infinity. Now infinities always get enclosed in a parenthesis, but looking at that 7, since x could be equal to 7 with that less than or equal to sign, I'm going to include it in a square bracket and that's my interval or that's my set in interval notation. Let's go ahead and graph this on the number line. So since x could be 7, that will be one of my end points here, and I'm going to graph it with a closed circle because x could be equal to it. Now x could also be anything that's less than 7 which I'm going to indicate with an arrow going all the way to negative infinity. And that's all for this one so let me know if you have any questions. Thanks for watching.

1. Equations & Inequalities

Linear Inequalities

College Algebra

1. Equations & Inequalities

Linear Inequalities

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Multiple Choice

Express the given set in interval notation and graph.
${$ $x$ $∣$ $x is less than or equal to 7$ $}$

(−∞,7]

A number line with a graph

[−∞,7]

A number line with a graph

(−∞,7)

A number line with a graph

[7, ∞)

A number line with a graph

Verified step by step guidance

Identify the inequality given in the set notation: $ x \leq 7 $. This means all numbers less than or equal to 7 are included in the set.

In interval notation, a square bracket $[$ is used to denote that the endpoint is included, while a parenthesis $()$ is used to denote that the endpoint is not included.

Since the inequality is $ x \leq 7 $, the number 7 is included in the set. Therefore, we use a square bracket at 7.

The set includes all numbers less than 7, extending indefinitely to the left. This is represented by $-\infty$ in interval notation, which always uses a parenthesis because infinity is not a specific number that can be reached.

Combine these observations to express the set in interval notation: $(-\infty, 7]$.