# Inequality Expressions

In mathematics, inequality expressions serve as fundamental tools for comparing the relative magnitudes of quantities. These expressions, often represented using symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), and ">=" (greater than or equal to), facilitate the description of relationships between numbers or variables. Through inequality expressions, mathematical concepts like order, magnitude, and relative positioning are succinctly communicated, forming the basis for solving various problems across disciplines such as algebra, calculus, and optimization.

Questions

- You have $60.00 in your wallet and want to buy some new CDs. If the CDs are $11.00 each, what number of CDs, x, can you buy? How do you write and solve an inequality?
- How do you express intervals as inequalities such as (-4,-2)?
- How do you write the following in interval notation: #x >2# OR #5<x#?
- Nate has scores of 85, 91, 89, and 93 on four tests. What is the least number of points he can get on the fifth test to have an average of at least 90?
- How do you write the inequality and solve given "twice a number increased by 3 is less than the number decreased by 4"?
- How do you write the inequality for "In 1955, the minimum wage in the U.S was $0.75 per hour"?
- How do you solve and write the following in interval notation: #7 ≥ x + 4# OR #x − 3 <2#?
- How do you graph #x>=5# on the number line?
- How do you write an inequality and solve given "two thirds of a number added to six is at least twenty two"?
- How do you graph #x< –2#?
- Papa's Pizza offers a party $4 per child with a $40 fee for the cake and playground supervisor. How do you write and solve an inequality that shows the number of children who can attend on a $76 budget?
- How do you graph #5>=a#?
- How do you solve #-0.16\geq 0.04a + 0.04#?
- How do you write an inequality and solve given "seven tenths of a number plus 14 is less than forty nine"?
- How do you write Seven less than 4 times a number is at most 44 and at least -24?
- Show that?: # |x| -|y| le |x-y| #
- What are the boundaries of x if #(2x-1)/(x+5) >= (x+2)/(x+3)?#
- A killer whale has eaten 75 pounds of fish today. It needs to eat at least 140 pounds of fish each day A bucket holds 15 pounds of fish. Identify an inequality that represents how many more buckets z of fish the whale needs to eat?
- How do you write the expression for: A number p is no greater than -6?
- How do you write the expression: Half of a number decreased by 7 is at least 5?