I would like an example of an inequality that uses both multiplication and addition properties of inequalities.

Question

I would like an example of an inequality that uses both multiplication and addition properties of inequalities.

Answer 1

I searched Google under the key words "inequality multiply add" to get these possible sources:

http://books.google.com/books?id=dfXeCUXeIDUC&pg=PA28&lpg=PA28&dq=inequality+multiply+add&source=web&ots=08SHKD0yGV&sig=H3fU36j3S3_4WXG0X3OJvoDHWbo&hl=en
http://www.analyzemath.com/Linear_Inequalities/Linear_Inequalities_Tutor.html
http://library.thinkquest.org/20991/alg2/eq.html
http://tutorial.math.lamar.edu/Classes/Alg/SolveLinearInequalities.aspx
http://www.sparknotes.com/testprep/books/sat2/math1c/chapter5section6.rhtml

In the future, you can find the information you desire more quickly, if you use appropriate key words to do your own search.

I hope this helps. Thanks for asking.

Answer 2

Sure! Let's create an example of an inequality that involves both the multiplication and addition properties:

Let's say we want to find an inequality that represents the following condition: "The product of a number and 4, increased by 7, is less than 20."

To do this, we can break down the condition into two parts:

1. "The product of a number and 4" - We can represent this as 4 times the unknown number, or 4x.

2. "Increased by 7" - We add 7 to the product, so the expression becomes 4x + 7.

Now, let's use the final part of the condition: "is less than 20." We can represent this by using the inequality symbol "<" to compare the expression (4x + 7) with 20.

Combining the parts, we have the following inequality:

4x + 7 < 20

This inequality uses both the multiplication property of inequalities (multiplying a number by a positive value does not change the direction of the inequality) and the addition property of inequalities (adding a positive value to both sides of an inequality does not change the direction of the inequality).

Remember, when solving inequalities involving multiplication and addition, it's crucial to follow the same rules as algebraic equations, such as applying inverse operations to isolate the variable on one side of the inequality.