DA Algebra 2016

2.2 Solving Inequalities Application Notes

Objective: You will understand how to write and solve a real-world inequality scenario.

Example 1: Verbal Phrases – Verbal problems containing phrases like greater than or less than can often be solved by using inequalities.
≤ / ≥

Write the correct inequality symbol with the key words below:

Inequality Key Words

  • At least - ______
  • No more than - ______
  • More than - ______
  • Less than - ______
  • At most - ______
  • Minimum - ______
  • Maximum - ______
  • Up to - ______
  • Fewer than - ______

Example 2: Underline the inequality phrases, then write and graph a linear inequality.
A. Jacob wants at least $200 in his bank account (b) by the end of the summer. / B. Hannah’s backpack (b) weighed less than 15 pounds.
C) The riders ( r ) have to be at least 4 feet tall to ride the roller coaster. / D. The cost of the purse (p) cannot be greater than $55.
E. Susie has no more than $25 to spend (s) at the mall. / E. A healthy baby weights (w) a minimum of 5.5 pounds.
Example 3: Real LifeModeling of an Equation or Inequality
  1. First – find a starting point (this is the initial amount)
  2. Second – find the rate of change ( the quantity that changes)
  3. Third – write an equation
  4. Fourth– look for the inequality word – write the inequality.

You are going to the amusement park for the day. The amusement part charges $7 for admission and $1.50 per ride.
A) You have $25 to spend. Write anequationto find x number of rides you can go on. / b) The most that you can spend is $25. Write and solve an inequality to find how many rides you can go on.
Inequality ______
Solve:
Answer: ______
Joe works at the ticket booth for a local movie theater. The movie theater has already sold $500 worth of tickets during a presale and will sell tickets for $10 each at the window.
C) If the movie theater earns $1000, how many tickets did they sell? Write anequation that represents x number of tickets sold. / D) Write and solve an inequality to find how many tickets must sell to make at least $1000.
Inequality ______
Solve:
Answer: ______
Casey is buying pizza for the family. It costs $12 plus $0.50 for each topping, tax included.
E) You have $22 to spend on pizza. Write anequation that represents the x number of toppings you can purchase. / F) She has $22.00 to spend on pizza. Write and solve an inequality to find the maximum number of toppings the pizza can have.
Inequality ______
Solve:
Answer: ______
Example 4: Writing a Real-Life situation from a graph.
Write a Real-life example that could reflect the graph below. Be sure to use an inequality word such as:
at least, at most, no more than, less than, maximum, minimum, up to, fewer than… when you write your description.
a)
/ b)

c)
/ d)

Practice Graphing from words

For each statement below graph an inequality
a.) All real numbers x that are less than or equal to 5.
/ b) All real numbers x that are greater than -3 and less than or equal to 4.

c) All real numbers x that are at most -4 or at least 3.
/ d) All real numbers x between -3 and 3 inclusive.