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Write an inequality that describes this graph.

Please explain HOW you got your answer, thanks a ton! :)

Write an inequality that describes this graph Please explain HOW you got your answer thanks a ton class=

Respuesta :

Jefrafra
To find the inequality, we need to remember our rules about what makes inequalities from number lines.

If the "dot" (initial point) is hollow, it is simply a "<" or ">" symbol. If the "dot" is filled in, it means that it includes that number and we should use a "≤" or "≥" symbol. In this case, our "dot" is filled, so we will be using a "≤" or "≥" symbol.

The second rule we must recall is that the "arrow" (symbol) points the direction that the line will go. In this case, our line is going left, so our "arrow" should point left (≤).

Using all of the logic above, we would be able to see that x≤1.

Answer:

z ≤ 1

Step-by-step explanation:

We know the following:

  • If the initial point is colored, then the only possible inequality signs are ≤ or ≥. However, if the initial point is not colored, then the possible inequality signs for the inequality is < or >.
  • If the line goes to the left of the initial point, it means that the initial point is greater than the numbers on the left of the initial point.
  • If the line goes to the right of the initial point, it means that the initial point is less than the numbers on the right of the initial point.
  • The inequality sign "≤" defines "less than or equal to"
  • The inequality sign "≥" defines "greater than or equal to"
  • The inequality sign "<" defines "greater than"
  • The inequality sign ">" defines "less than"

We can observe that:

In the inequality, we can see that the initial point of the inequality is colored. Therefore, the possible inequality signs for the inequality shown on graph are ≤ or ≥. Let us start setting our inequality.

  • ⇒ _ ≤ or ≥ _

We can see that the inequality line shown on the graph, goes to the left. Therefore, the line shown on the graph defines that the initial point is greater than the numbers on the left of the number line.

  • ⇒ _ ≥ _

Since "1" is the initial point and is greater than or equal to the numbers on the inequality, we can put "1" on the L.H.S of the inequality. Now,

  • ⇒ 1 ≥ _

[Optional] Write the numbers, that are less than 1, on the R.H.S of the inequality. Then, we get the following inequality:

  • ⇒ 1 ≥ 0, -2, -4, -6...

[Optional] Include "1" in the series as ≤ means greater than or equal to.

  • ⇒ 1 ≥ 1, 0, -2, -4, -6...

Let us assume that the numbers less than and equal to 1, be known as z.

  • ⇒ 1 ≥ 1, 0, -2, -4, -6...
  • ⇒ 1 ≥ z

Therefore, the inequality that represents the graph is z ≤ 1.

Learn more about inequalities: https://brainly.com/question/26107931

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