Warm Up 12/5-Inequalities in Real-Life Scenarios

Front

What is an inequality?

Back

An inequality is a mathematical statement that shows the relationship between two expressions that are not equal, using symbols such as <, >, ≤, or ≥.

Front

How do you represent a real-life scenario with an inequality?

Back

You identify the quantities involved, determine the relationship between them, and express it using an inequality symbol.

Front

What does the symbol '≥' mean in an inequality?

Back

The symbol '≥' means 'greater than or equal to', indicating that the value on the left is either greater than or equal to the value on the right.

Front

What does the symbol '≤' mean in an inequality?

Back

The symbol '≤' means 'less than or equal to', indicating that the value on the left is either less than or equal to the value on the right.

Front

How do you solve the inequality 500 - 25x ≥ 200?

Back

To solve, subtract 500 from both sides: -25x ≥ -300. Then divide by -25 (remember to flip the inequality): x ≤ 12.

Front

What is the first step in solving the inequality 5x + 10 ≥ 100?

Back

Subtract 10 from both sides: 5x ≥ 90.

Front

How do you find the maximum number of hours a DJ can play if the total cost must be under $600?

Back

Set up the inequality 125x + 55 < 600 and solve for x.

Front

What is the relationship between the price of a jacket and a skirt in the inequality 3x + 20 ≤ 120?

Back

The price of the jacket is $20 more than three times the price of the skirt.

Front

How do you interpret the inequality 1.50x + 10 ≤ 40 in a real-life context?

Back

It represents the total amount Daniel can spend at the fair, where 10 is the admission cost and 1.50x is the cost of rides.

Front

What is the significance of the constant term in an inequality?

Back

The constant term represents fixed costs or values that do not change, which can affect the overall relationship expressed by the inequality.