Scenario: Shopping Budget - Solve inequalities to stay within your budget!
Xiao Ming has $80 to spend. He wants to buy a backpack for $35 and some notebooks. If each notebook costs $x, how many notebooks can he buy without exceeding his budget?
Problem: Backpack cost + Notebook cost ≤ Total budget
Step 1: Write the inequality
35 + x × n ≤ 80
Where n = number of notebooks
Step 2: Solve for n
x × n ≤ 80 - 35
x × n ≤ 45
n ≤ 45/x
Step 3: Example with specific price
If x = $5: n ≤ 45/5 = 9
He can buy at most 9 notebooks
Answer: n ≤ 45/x notebooks (where x is the price per notebook)
<
Less than
Example: x < 5
≤
Less than or equal to
Example: x ≤ 5
>
Greater than
Example: x > 3
≥
Greater than or equal to
Example: x ≥ 3
Open circle at 4, arrow pointing right (x > 4)
Closed circle at 7, arrow pointing left (x ≤ 7)
Solve: 2x + 7 > 15
Solution:
2x + 7 > 15
2x > 15 - 7
2x > 8
x > 4
Solve: (x/3) - 2 ≤ 1
Solution:
(x/3) - 2 ≤ 1
x/3 ≤ 1 + 2
x/3 ≤ 3
x ≤ 9
Solve: 3x - 5 < 10
Your solution:
A student has $50. She wants to buy some books at $8 each and still have at least $10 left. How many books can she buy?
Your solution: