contestada

For tropical fish, aquarium water should be set to 76° F with an allowance of 4°.

a. Explain how to write an absolute value equation to represent this situation.

b. Explain the steps to solve the absolute value equation. What do the solutions represent?

Respuesta :

Using absolute value, it is found that:

  • The absolute value equation that models the situation is: [tex]|T - 76| = 4[/tex]
  • The two solutions, [tex]T = 72[/tex] and [tex]T = 80[/tex], mean that the temperature of the aquarium water must be between these two values.

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  • The absolute value function is defined by:

[tex]|x| = x, x \geq 0[/tex]

[tex]|x| = -x, x < 0[/tex]

  • It measures the distance of a point x to the origin.

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Item a:

The temperature should be set to 76ºF with an allowance of 4ºF, thus, the absolute value of the difference between the temperature T and 76 should be 4, that is:

[tex]|T - 76| = 4[/tex]

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Item b:

  • Here, it is needed to solve the equation.

There are two solutions:

[tex]T - 76 = 4[/tex]

[tex]T = 80[/tex]

Or also:

[tex]T - 76 = -4[/tex]

[tex]T = 72[/tex]

  • The two solutions, [tex]T = 72[/tex] and [tex]T = 80[/tex], mean that the temperature of the aquarium water must be between these two values.

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