Mathematics, 03.08.2019 06:00 jrich5111

Which type of absolute value inequality requires the use of a compound inequality to reach the solution?

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Let's approach this problem by considering simple cases. We will consider two kinds of absolute value inequalities, depending on whether the absolute value is less than or greater than a constant.

$|x| \geq 2$

Let's consider this first case where the absolute value of x should be greater than or equal to 2. Intuition would tell us that if x is positive, it should be greater than or equal to 2 while if x is negative it should be less than or equal to -2. These two solutions cannot be combined together. This will be true for every expression with a greater than symbol favoring the absolute value. Answers for this case will just be written as

$x \geq 2$ or $x \leq -2$

Now let's consider the following case:

$|x| \leq 2$

For this expression, our x needs to be less than or equal to 2 if it's positive and greater than or equal to -2 if it's negative. We'll notice that these two conditions actually intersect! It is possible to combine the answer into a compound inequality. A compound inequality is an expression where two statements are joined by AND instead of OR (like what happened in the previous case). For this case we'll have the following

$-2 \leq |x| \leq 2$

ANSWER: Inequalities where 'greater than' symbols favor the CONSTANT will make use of compound inequalities.

Answer from: Quest

answer: what in the world is this

step-by-step explanation:

Answer from: Quest

the number of possible outcomes that do not show a 1 on the first spinner and show the number 4 on the second spinner is 2.

spinner 1 spinner 2

1 1

1 2

1 3

1 4

2 1

2 2

2 3

2 4 = not 1, and 4

3 1

3 2

3 3

3 4 = not 1, and 4

only 2 outcomes have passed the given condition.

step-by-step explanation:

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