How to write absolute value inequalities from word problems?

How to write absolute value inequalities from word problems?

Absolute value inequalities can be confusing at first, but once you understand the process, they become much easier to work with. Here’s a step-by-step guide on how to write absolute value inequalities from word problems:

1.

What does absolute value represent?

The absolute value of a number is its distance from zero on the number line. It is always positive or zero.

2.

What is an absolute value inequality?

An absolute value inequality is an inequality that involves the absolute value of an expression.

3.

How to write an absolute value inequality from a word problem?

1. Identify the quantity that should be enclosed in absolute value bars.
2. Write the inequality without absolute value bars.
3. Set up two inequalities, one for when the expression inside the bars is positive and another for when it is negative.

4.

Can you provide an example of a word problem where we write an absolute value inequality?

Sure! Let’s say you have a word problem where the distance between a number and 5 is less than 3. The inequality would be |x – 5| < 3. 5.

How do we write the two inequalities for the previous example?

The two inequalities would be x – 5 < 3 and x - 5 > -3.

6.

What do we do next after setting up the two inequalities?

Solve each inequality separately to find the possible values of x that satisfy both conditions.

7.

How do we know if an method is positive or negative?

If the expression inside the absolute value bars is greater than or equal to zero, it is positive. If it is less than zero, it is negative.

8.

What happens if the word problem involves greater than or equal to instead of just greater than?

In that case, you would use the symbols ≤ and ≥ in the inequalities instead of just < and >.

9.

What happens if the word problem involves the absolute value being greater than or equal to a certain number?

Instead of < or >, you would use ≥ or ≤ in the inequalities.

10.

Can absolute value inequalities have multiple solutions?

Yes, absolute value inequalities can have multiple solutions, especially when the absolute value involves more than one expression.

11.

What if the word problem involves inequalities with variables on both sides of the absolute value?

In that case, you may need to simplify the expression first before setting up the absolute value inequalities.

12.

Are there any common mistakes to avoid when writing absolute value inequalities from word problems?

One common mistake is forgetting to set up two separate inequalities for the positive and negative cases. Make sure to consider both possibilities when writing absolute value inequalities.

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