Respuesta :
Answer:
Max value for t is -1 and minimum value for t is -5
Step-by-step explanation:
Make two inequalities in regards to absolute value and solve both for t:
t+3<=2 and t+3>=-2
t<=-1 and t>=-5
The compound inequality would be -1>=t>=-5
Solving the absolute value inequality, it is found that:
- The minimum value is t = -5.
- The maximum value is t = -1.
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- The absolute value measures the distance of a point to the origin.
- The inequality [tex]|f(x)| \leq a[/tex] represents the set of values of x for which the distance of points f(x) and the origin are at most a. The solution is:
[tex]-a \leq f(x) \leq a[/tex]
In this problem, the inequality is:
[tex]|t + 3| \leq 2[/tex]
Thus, the solution is:
[tex]-2 \leq t + 3 \leq 2[/tex]
[tex]-2 \leq t + 3[/tex]
[tex]t + 3 \geq -2[/tex]
[tex]t \geq -5[/tex]
[tex]t + 3 \leq 2[/tex]
[tex]t \leq -1[/tex]
Then:
- The minimum value is t = -5.
- The maximum value is t = -1.
A similar problem is given at https://brainly.com/question/24005819
