Question

What are the minimum and maximum values of t for which |t + 3| ≤ 2

Answer 1

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

Answer 2

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 $|f(x)| \leq a$ 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:

$-a \leq f(x) \leq a$

In this problem, the inequality is:

$|t + 3| \leq 2$

Thus, the solution is:

$-2 \leq t + 3 \leq 2$

$-2 \leq t + 3$

$t + 3 \geq -2$

$t \geq -5$

$t + 3 \leq 2$

$t \leq -1$

Then:

• The minimum value is t = -5.
• The maximum value is t = -1.

A similar problem is given at https://brainly.com/question/24005819