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What is the solution set for StartAbsoluteValue y minus 9 EndAbsoluteValue less-than-or-equal-to 12:A?


y greater-than-or-equal-to 3 or y less-than-or-equal-to 21
Negative 3 less-than-or-equal-to y less-than-or-equal-to 21
y greater-than-or-equal-to negative 3 or y less-than-or-equal-to 21
3 less-than-or-equal-to y less-than-or-equal-to 21

Respuesta :

Using the absolute value concept, it is found that the solution is:

  • [tex]-3 \leq y \leq 21[/tex]
  • Which is given by the second option.

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  • The absolute value of a point, or of a function, measures it's distance to the origin.

  • The inequality given by:

[tex]|y - 9| \leq 12[/tex]

  • The distance to the origin is of at most 12 between -12 and 12, thus:

[tex]-12 \leq y - 9 \leq 12[/tex]

  • We have to solve both inequalities, and find the intersection.

[tex]-12 \leq y - 9[/tex]

[tex]-y \leq 3[/tex]

[tex]y \geq -3[/tex]

[tex]y - 9 \leq 12[/tex]

[tex]y \leq 21[/tex]

  • The intersection is values of y between -3 and 21(and logical operator, not or), inclusive, thus: [tex]y \geq -3[/tex] and [tex]y \leq 21[/tex], that is: [tex]-3 \leq y \leq 21[/tex]

A similar problem, involving absolute value, is given at https://brainly.com/question/24734454

Nolfy

Answer:

B: -3 ≤ y ≤21

Step-by-step explanation:

Ver imagen Nolfy

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