Applications with Inequalities

Key Questions

• What inequalities are used to show "at least" or "no more than"?

  Examples

  #x# is at least #2#. #<=># #x ge 2#

  #x# is no more than #5#. #<=># #x le 5#

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  I hope that this was helpful.

  Wataru · 5 · Nov 5 2014
• When do you use inequalities to solve word problems?

  When we need to make some calculated number less than (or greater than, or not more than or not less than) some fixed number. Or when we need to made one calculated number less (or whatever) than another calculated number.

  For instance, Suppose I want to go into the tee-shirt printing business. If I know that it will cost me #$140# for material plus #$12# per shirt printed, and I have #$600# that I can spend getting started, what is the maximum number of tee-shirts I can produce?

  This means solving: #12x+140<=600#.

  (OK, it's not the best possible example, but that's the kind of thing we need it for in algebra. There are other kinds of problems in calculus that involve increasing and decreasing quantities.)

  Jim H · 1 · Mar 6 2015

• When do you use inequalities to solve word problems?
• What inequalities are used to show "at least" or "no more than"?
• How do you write an inequality statement to show that you must be at least 48 inches tall to ride the roller coaster?
• What is the inequality statement to show that Charlie needs more than $1,800 to purchase a car?
• How do you write an inequality statement to show that ninety percent of some number is at most 45?
• What must the length of a rectangle be if the with is 12 inches and the perimeter is at least 180 inches? :
• Liz earns a salary of $2,100 per month, plus a commission of 5% of her sales. She wants to earn at least $2,400 this month. How do you write an inequality to find amounts of sales that will meet her goal?
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