What you’ll learn
Create linear inequalities.
Key idea
Upper and lower spending conditions have different directions; strict and inclusive wording differ at equality.
Worked example
Enter the exact value or ordered values in the format requested below.
Entry costs 8 dollars once and each ride costs 2 dollars. x is nonnegative whole-number rides; spending must be more than 18 dollars. Create the cost inequality without solving it.
- Total cost 8+2x has dollar units; more than translates to >.
- Model 8+2x>18; equality at 18 dollars is excluded. Count 5 gives exactly the boundary, so endpoint inclusion follows the wording.
Answer: 8+2x>18
Quick Check
Choose which candidate representation satisfies the requirements of 'Create linear inequalities' and justify the choice.
Entry costs 8 dollars once and each ride costs 3 dollars. x is nonnegative whole-number rides; spending must be at most 23 dollars. Select the model whose boundary spending is included.